Answers
Answer:
- [tex]\frac{2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Using the identity and the exact value
csc x = [tex]\frac{1}{sinx}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
- 120° is in the third quadrant where sin < 0 , then
csc - 120° = - sin60° , then
csc - 120°
= [tex]\frac{1}{-sin60}[/tex]
= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]
= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )
= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= - [tex]\frac{2\sqrt{3} }{3}[/tex]
The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
We know that the cosecant function is defined as the reciprocal of the sine function:
cosec (θ) = 1 / sin(θ)
Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).
We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,
sin(-120°) = -sin(120°)
We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).
Using the same logic as before, we get:
sin(-240°) = -sin(240°)
Now , from the trigonometric relations , we get
Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:
sin(-240°) = -sin(-120°)
Therefore, we have:
sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)
Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:
In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.
Therefore, sin(240°) = O/H = (√3)/2.
Finally, we can use the definition of the cosecant function to find cosec(-120°):
cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.
Hence , cosec(-120°) is equal to (2√3)/3.
To learn more about trigonometric relations click :
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Related Questions
4. Convert 23 miles per hour to kilometers per minute. (1 mile = 1.609 kilometers)
Answers
Answer:
Ewan ko lng po when you find someone ma mas better less sa kanya
A boutique was having a 20% storewide sale.Erica bought 2 dresses which originally cost $80 each.How much savings did Erica enjoy?
Answers
Answer: $32
Step-by-step explanation:
Since the boutique was having a 20% storewide sale and Erica bought 2 dresses which originally cost $80 each, therefore the sale for each dress will be:
= $80 - (20% × $80)
= $80 - (0.2 × $80)
= $80 - $16
= $64
Therefore, on each dress Erica saves $16. The amount of savings enjoyed will then be:
= $16 × 2
= $32
PLEASE PLEASE HELP ILL GIVE BRAINLY
Answers
Answer:
In this case, we can do substitution.
Step-by-step explanation:
For the first one, (s - t)(x) = ((x - 5) - 4x^2)(x) = x^2 - 21x
For the second one, (s*t)(x) = ((x - 5) *4x^2)(x) = 4x^4 - 20x^3
And for the last one, (s+t)(-2) = ((x - 5) + 4x^2)(-2) = -8x^2 - 2x + 10
Hope your happy with the answer :)
PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?
A. (12, 8)
B. (3, 5)
C. (-3, 3)
D. (0, 4)
please don’t use this for points.
Answers
Answer:
A.............
Step-by-step explanation:
. ..........
Answer:
C. (3,3)
Step-by-step explanation:
When These equations are both graphed the solution for these equations when they intersect is (-3,3)
Please help thank you!
Answers
Answer:
2
Step-by-step explanation:
X^2+Y^2=4=2^2
someone help me for this algebra task please
Answers
Answer:
The answer is
[tex]4+ x[/tex]
Using the definition of linear equation,
[tex]y = 4 + x[/tex]
Is the answer.
Factor using the perfect squares method:
x^2 - 3x + 16
Answers
Answer:
what are the answer choice?
Step-by-step explanation:
The ages of Raju and Ravi are in the ratio 3:4 Four years from now the ratio of their ages will be 4:5 Find their present ages
Answers
Answer: Their present age is 12 and 16.
Step-by-step explanation:
Let the required age be 3x and 4x
so
(3x+4)/(4x+4) = 4/5
5(3x+4) = 4(4x+4)
or, 15x + 20 = 16x + 16
or, 15x - 16x = 16-20
or, -x = -4
so, x = 4
now,
3x = 3*4 = 12
4x = 4*4 = 16
Que cantidad se obtiene al resolver la siguiente operacion: [4+{(2-5)2-4(7-5)3+2(15/3)}]- Raiz cuadrada de 16
Answers
Respuesta:
-13
Explicación paso a paso:
Dada la ecuación:
[4 + {(2-5) ²-4 (7-5) ³ + 2 (15/3)}] - Raíz cuadrada de 16
La raíz cuadrada de 16 se escribe como √16
[4 + {3² - 4 (2³) + 2 (5)} - √16
4 + {9 - 4 (2 * 2 * 2) + 10} - 4
4 + {9 - 4 (8) + 10} - 4
4 + {9 - 32 + 10} - 4
4 - 13 - 4
= -13
A company is selling specialty ice cream. Their profit is modeled by the equation p(x) = x2 + 3, where x represents the number of cartons sold. Their cost to make the carton is represented by c(x) = -3x + 24, where x represents the number of cartons produced.
A. What does it mean to find the solution to this system?
B. What is the solution to the system? How did you find the solution?
C. What does the solution mean in context of the problem?
D. How do you solve this system when x does not stand for the same thing? What system are you referring to?
Answers
Answer:
The given function for the profit of the company is p(x) = x² + 3
The function for the cos of the company, c(x) = -3·x + 24
Where;
x = The number of cartons sold
A. To find the solution of the system means to find the number of cartons sold at which the profit and cost are equal
B. The solution of the system can be found by equating both functions as follows;
p(x) = c(x)
Therefore;
x² + 3 = -3·x + 24
∴ x² + 3 + 3·x - 24 = 0
x² + 3·x - 21 = 0
x = (-3 ± √(3² - 4×1×(-21)))/(2 × 1)
∴ x = (-3 ± √(93))/2
x = (-3 + √(93))/2 ≈ 3.32 or x = (-3 - √(93))/2 ≈ -6.32
Therefore, the possible solution is x = (-3 + √(93))/2 ≈ 3.32
C. The solution means that when the company sells about 3 cartons of specialty ice, the cost to make the carton and the profit from selling the cartons will be approximately equal
D. Part 1
To solve the system, we rewrite the functions using common variables, to obtain a consistent system of equations
Part 2 Inconsistent system of equations
When x does not stand for the same thing in both equations, we have an inconsistent system of equations and there are no solutions
Step-by-step explanation:
Lily owed Megan $129.42. So far, she has paid Megan $32.56.
The remaining amount Lily has yet to pay Megan is $
Answers
Answer: $96.86
Step-by-step explanation:
Lily owed megan = $129.42
she has paid megan = $32.56
The remaining amount Lily has yet to pay Megan = $129.42 - $32.56 = $96.86.
Please mark me the brainliest
at what speed was jo walking for the first 30 minutes
Answers
Answer:
Bro a normal speed of a human is 3km/hr
And I don't know the speed of jo
Because u haven't written full question
Step-by-step explanation:
Please Mark me brainliest
Help me solve this problem please
Answers
Answer:
A 2,3,6 :)
Step-by-step explanation:
thats answer corect me if im wrong hope it help
Find all possible values of α+
β+γ when tanα+tanβ+tanγ = tanαtanβtanγ (-π/2<α<π/2 , -π/2<β<π/2 , -π/2<γ<π/2)
Show your work too. Thank you!
Answers
Answer:
[tex]\rm\displaystyle 0,\pm\pi [/tex]
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
===========================
we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]
factor out tanγ:
[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]
divide both sides by tanαtanβ-1 and that yields:
[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]
multiply both numerator and denominator by-1 which yields:
[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]
recall angle sum indentity of tan:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]
let α+β be t and transform:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]
remember that tan(t)=tan(t±kπ) so
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]
therefore when k is 1 we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]
when is 0:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]
likewise by Opposite Angle Identity we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]
and we're done!
Answer:
-π, 0, and π
Step-by-step explanation:
You can solve for tan y :
tan y (tan a + tan B - 1) = tan a + tan y
Assuming tan a + tan B ≠ 1, we obtain
[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]
which implies that
y = -a - B + kπ
for some integer k. Thus
a + B + y = kπ
With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.
It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so
[tex]B=\frac{\pi }{2} - a + k\pi[/tex]
but with the given limitation we must have k = 0, because 0 < π/2 - a < π.
On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again
k = 0, so we obtain
[tex]\frac{\pi }{2} - a=-a[/tex]
a contradiction.
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.
Answers
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=5
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
5²+5²=h²
50=h²
h=[tex]\sqrt{50}[/tex]
x=[tex]\bold{5\sqrt{2}}[/tex]
Which is the graph of the linear inequality x - 2y > -6?
-10-
2
108
0
o
Answers
Answer:
the fourth option
Step-by-step explanation:
1/2x - 2y > -6
1/2x + 6 > y
or
y < 1/2x + 6
so, the solution is all the y values smaller (= below) the line function.
and because it is "<" and not "<=" the line itself is not included
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right
Answers
So the interior angle would still be 135
The function graphed to the left is
function.
and continues
The curve has
infinitely in one direction.
each
Each y-value is
corresponding x-value.
Answers
Answer: There is a circular
Step-by-step explanation:
Answer:
he function graphed to the left is
✔ a square root
function.
The curve has
✔ one distinct endpoint
and continues infinitely in one direction.
Each y-value is
✔ the square root of
each corresponding x-value.
Step-by-step explanation:
Complete the following proof by dragging and dropping the correct reason in the spaces below
Answers
Answer:
2
Step-by-step explanation:
1+1 = 2
So the answer is 2
hope this helps
Find the length of the mid segment (median)
Answers
Answer:
13
Step-by-step explanation:
Median of a trapezoid = sum of 2 bases divided by 2
Bases = 10 and 16
Median = (10 + 16)/2
10 + 16 = 26
26/2 = 13
Median = 13
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
Answers
Answer:
-2,-1,0,1,2
Step-by-step explanation:
Answer:
-2.0
0,0
Step-by-step explanation:
i just did the test
find the sum of the series
√2 - 2 + 2√2 +__+64√2.
Answers
Step-by-step explanation:
The question is not clear to me
Find the number of degrees in the measure of angle x
Answers
Answer: x = 82°
Step-by-step explanation:
The angle on the other side of 108° can be calculated as 180° - 108° = 72°
All angles within a triangle add up to 180°, so the x-value can be found as:
x = 180° - 72° - 26° = 82°
asap help answer ---------
Answers
Answer:
[tex]C(n)=30-20n[/tex]
Step-by-step explanation:
Arithmetic sequence given in the question is,
10, -10, -30, -50........
Explicit formula of an Arithmetic sequence is given by,
[tex]C(n)=C(1)+(n-1)d[/tex]
Here, [tex]C_1=[/tex] First term
[tex]n=[/tex] number of terms
[tex]d=[/tex] common difference
From the given sequence,
[tex]C(1)=10[/tex]
[tex]d=-10-10[/tex]
[tex]=-20[/tex]
Substitute the values in the formula,
[tex]C(n)=10+(n-1)(-20)[/tex]
[tex]C(n)=10-20n+20[/tex]
[tex]C(n)=30-20n[/tex]
What is X if line a and b are parallel
Answers
Answer:
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
8x = 180 - 148 [ corresponding angles are equal ]
8x = 32
x = 4
Nissa is going to plant 485 485485 trees this year. If Nissa plants 5 55 orchards of trees, how many trees will be in each orchard?
Answers
Answer:
There will be 97 trees in each orchard.
Step-by-step explanation:
Given that,
Nissa is going to plant 485 trees this year.
Nissa plants 5 orchards of trees.
We need to find the number of trees in each orchard. Let it is n. So, we can find it as follows :
[tex]n=\dfrac{485}{5}\\\\n=97[/tex]
So, there will be 97 trees in each orchard.
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money. Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answers
Answer:
25m + 10b = 400
Step-by-step explanation:
Total amount that can be earned = $ 400
Amount earned on mowing a lawn = $ 25
Amount earned per hour on babysitting = $10
Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m
Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b
Using the values from above, we can set up the equation as:
400 = 25m + 10b
or
25m + 10b = 400
This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Hope this helps have a good day
Grafico de deportes: fútbol 30%, atletismo 25%, tenis 5%, voleibol 10%, basquetbol 20%. Si 165 jóvenes prefieren el fútbol ¿cuantos prefieren el basquetbol?
Answers
Answer:
33 jóvenes prefieren el basquetbol.
Step-by-step explanation:
Hay 165 jóvenes.
De estos, 20% prefieren el basquetbol.
¿cuantos prefieren el basquetbol?
20% de 165, entonces:
[tex]20\% = \frac{20}{100} = 0.2[/tex]
[tex]0.2*165 = 33[/tex]
33 jóvenes prefieren el basquetbol.
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
Sequence 1
Sequence 2
Ordered Pairs
PLZ ANSWER FOR Brainiest
Answers
Answer:
1×2+1=3
3×2+1=7
7×2+1=15
15x2+1=31
31×2+1=63
40÷2+4=24
24÷2+4÷16
16÷2+4=12
12÷2+4=10
10÷2+4=9
HELP ASAP!!!
The circle graph shows the percentage of visitors at a
convention who ordered various flavors of juice. There were 700
visitors at the convention.
About how many visitors ordered grape juice or apple juice?
Enter your answer in the box.
Answers
Step-by-step explanation:
40+24+11+8+17= 100
100 - 700
24 - ?
24×700/100
= 168 visitors ordered apple juice
100-700
11-?
11×700/100
=77 people ordered grape juice
