Mathematics College

Look at the figure:

An image of a right triangle is shown with an angle labeled x.

If tan x° = a divided by 4 and cos x° = 4 divided by b what is the value of sin x°?

sin x° = 4b
sin x° = b divided by a
sin x° = 4a
sin x° = a divided by b

Answers

Answer 1

By using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].

What are trigonometric functions?

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

[tex]\sin \text{x}^\circ= \ ?[/tex]

[tex]\tan \text{x}^\circ=\dfrac{\text{a}}{4}[/tex]

[tex]\cos \text{x}^\circ=\dfrac{4}{\text{b}}[/tex]

Formula to find [tex]\sin \text{x}^\circ[/tex]

[tex]\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}[/tex]

Therefore, by using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].

To know more about trigonometric functions, visit:

https://brainly.com/question/31540769

Look At The Figure:An Image Of A Right Triangle Is Shown With An Angle Labeled X.If Tan X = A Divided

Related Questions

Solve (9th grade math)

Answers

Answer:

1. Geometric Sequence Equation for Table A:

[tex]\boxed{\tt a_n = a_1 \times r^{(n-1)}}[/tex]

2. Arithmetic Sequence Equation for Table B:

[tex]\boxed{\tt a_n = a_1 + (n-1) \times d}[/tex]

3.

20th term for Geometric Sequence:
[tex]\boxed{\tt a_{20} = a_1 \times r^{19}}[/tex] 20th term for Geometric Sequence:
[tex]\boxed{\tt a_{20} = a_1 + 19\times d}[/tex]

Step-by-step explanation:

1. Geometric Sequence Equation for Table A:

The geometric sequence equation is given by the formula:

[tex]\tt \[a_n = a_1 \times r^{(n-1)}\][/tex]

where:

[tex]\tt \(a_n\)[/tex] represents the nth term of the sequence.[tex]\tt \(a_1\)[/tex] is the first term of the sequence.[tex]\tt \(r\)[/tex] is the common ratio.

For Table A, since we don't have the actual values, we can represent the equation as:

[tex]\boxed{\tt a_n = a_1 \times r^{(n-1)}}[/tex]

[tex]\hrulefill[/tex]

2. Arithmetic Sequence Equation for Table B:

The arithmetic sequence equation is given by the formula:

[tex]\tt a_n = a_1 + (n-1) \times d[/tex]

where:

[tex]\tt \(a_n\)[/tex] represents the nth term of the sequence.[tex]\tt \(a_1\)[/tex] is the first term of the sequence.[tex]\tt \(d\)[/tex] is the common difference.

For Table B, since we don't have the actual values, we can represent the equation as:

[tex]\boxed{\tt a_n = a_1 + (n-1) \times d}[/tex]

[tex]\hrulefill[/tex]

3. Finding Term 20 for both sequences:

In order to find the 20th term for both sequences, we need the actual values for [tex]\tt \(a_1\), \(r\)[/tex] and d.

in the case of Table A

[tex]\tt a_{20} = a_1 \times r^{(20-1)}[/tex]

[tex]\boxed{\tt a_{20} = a_1 \times r^{19}}[/tex]

in the case of Table B.

[tex]\tt a_{20} = a_1 + (20-1) \times d[/tex]

[tex]\boxed{\tt a_{20} = a_1 + 19\times d}[/tex]

By using this formula, we can easily fill up the box.

Differentiate the function. Then find an equation of the tangent line at the indicated point on the graph of the function.

Answers

Answer:

The derivative of the function:

[tex]f'(x)=-\dfrac{1}{2\sqrt{5-x} }[/tex]

The tangent line of the function at the given point:

[tex]y=-\dfrac{1}{6}x-\dfrac{25}{3}[/tex]

Step-by-step explanation:

Find the equation of the tangent line of the given function using the given point.

[tex]f(x)=6+\sqrt{5-x}; \ (x,y)=(-4,9)[/tex]

[tex]\hrulefill[/tex]

To find the equation of the tangent line to a function at a given point, follow these step-by-step instructions:

Step 1: Identify the point of tangency

Determine the x-coordinate of the point of tangency. Let's call it x₀.Find the corresponding y-coordinate of the point of tangency. Let's call it y₀.

Step 2: Find the derivative of the function

Calculate the derivative of the given function. Let's denote it as f'(x).

Step 3: Substitute the x-coordinate into the derivative

Replace the variable x in the derivative function f'(x) with the x-coordinate of the point of tangency (x₀).Evaluate the derivative at x₀ to find the slope of the tangent line. Let's denote it as m.

Step 4: Write the equation of the tangent line

Use the point-slope form of a line: y - y₀ = m(x - x₀).Substitute the values of m, x₀, and y₀ into the equation.Simplify and rearrange the equation to obtain the final form.

Step 5: Optional - Simplify the equation

If necessary, simplify the equation by performing any algebraic manipulations.

Step 6: Optional - Verify the equation

Check the obtained equation by plugging in other points along the tangent line and ensuring they satisfy the equation.

[tex]\hrulefill[/tex]

Step 1:

[tex](x_0,y_0) \rightarrow (-4,9)[/tex]

Step 2:

[tex]f(x)=6+\sqrt{5-x}\\\\\\\Longrightarrow f(x)=6+(5-x)^{1/2}\\\\\\\Longrightarrow f'(x)=\dfrac{1}{2} (5-x)^{1/2-1} \cdot -1\\\\\\\therefore \boxed{f'(x)=-\dfrac{1}{2\sqrt{5-x} } }[/tex]

Step 3:

[tex]f'(x)=-\dfrac{1}{2\sqrt{5-x} } ; \ (-4,9)\\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2\sqrt{5-(-4)} } \\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2\sqrt{9}} \\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2(3)} \\\\\\\therefore \boxed{ f'(-4)=m=-\dfrac{1}{6} }[/tex]

Step 4 and 5:

[tex]y-y_0=m(x-x_0)\\\\\\\Longrightarrow y-9=-\dfrac{1}{6}(x-(-4)) \\\\\\\Longrightarrow y-9=-\dfrac{1}{6}(x+4) \\\\\\\Longrightarrow y-9=-\dfrac{1}{6}x-\dfrac{2}{3}\\\\ \\\therefore \boxed{\boxed{ y=-\dfrac{1}{6}x-\dfrac{25}{3}}}[/tex]

Thus, the problem is solved.

Find the original slope of (-6,-1) and (0,3)

Answers

The original slope would be -2/3

Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Other Questions
The company you work for is the only supplier of specialty precision machinery for heavy equipment manufacturers. You are the chief operating officer and you have to determine the optimal production level to maximize profit. You have asked your analysts to gather information for you and below are their findings:Fixed costs are 3,000 and variable costs are 100 Q + Q^2/2.The demand curve is estimated to be:P = 500 - 1.5 QSolve for the optimal output and price levels. What will be your firms profit at this output and price level? Illustrate graphically how you came up with these results and compare it to any other equilibrium point under different circumstances.Is this equilibrium good for the firm? Why or why not? Is it good for consumers? Explain your answers in detail. What are the potential costs and benefits of this equilibrium to both parties? Is society as a whole better or worse off?Your firm has been an attractive investment for portfolio managers. Explain why that is the case. What would be the long-term risks that your firm could be facing? As explained in this class, in an asymmetrical joint venturewhere one firm is larger and older and the other firm is smallerand younger, the larger and older firm would most likely becontributing _ a) The transfer function of a third-order normalised lowpass Chebyshev filter is given by 0.5 H(s) = (s +0.5) (s +0.5s +1) Find the ripple level of this filter in dB. Which of the following symbiotic mutualisms involves a fungus?A.lichensB.corals and zooxanthellaeC.legume-Rhizobium interactionsD.gut microbe-ruminant interactions collins and quillian (1969) suggest that information is organized The velocity v of a particle moving in the xy plane is given by v = (6t - 4t ^ 2) * l + 1j . Here v is in meters per second and t(>0) is in seconds () What is the acceleration when t = 3 * 57; Box m/s^ 2 1+ Box m/s^ 2 1+ Box m/s^ 2 1 k () When is the acceleration zero? (Enter never appropriate.) ) When is the velocity zero? (Enter never if appropriate.) ) When does the speed equal 10 m/s? If a parameterized curve r (t) satisfies the equation r'(t). r"(t) = 0 for all t, what does this mean geometrically?o The parameterized curve has constant speed. o The curve stays on a sphere centered at the origin. o The curve is a circle or part of a circle. o None of these Iff(x)=3x25x+7, findf(2)Use this to find the equation of the tangent line to the parabolay=3x25x+7at the point(2,9). The equation of this tangent line can be written in the formy=mx+bwheremis: and wherebis: why did the kings color change, his thoughts alarm him, his limbs give way, and his knees knock together when he saw the handwriting appear on the wall? Act II, Scene ii opens with a series of soliloquies before Romeo and Juliet speak to each other. What is the best description of the effect these soliloquies have on the scene?The soliloquies make the entire scene feel more realistic. The soliloquies make the balcony scene more tragic.The soliloquies create a romantic, intimate mood. The soliloquies suggest that the scene is not real, but only a dream. Two point charges q 1 and q 2 are 3.25 m apart, and their total charge is 20C. Note that you may need to solve a quadratic equation to reach your answer. (a) If the force of repulsion between them is 0.077 N, what are the two charges ( in C) ? smaller value C largr value \& C (b) If one charge attracts the other with a force of 0.365 N, what are the two charges (in C )? srraller value C larger value xC Cherboneau Novelties produces drink coasters (among many other products). During the current year (year O), the company sold 536,000 units (packages of 6 coasters). In the coming year (year 1), the company expects to sell 572,000 units, and, in year 2, it expects to sell 816,000 units. The target ending finished goods inventory for each month is equal to the next month's sales. However, because of production issues, the ending inventory in the current year is expected to be only 20,000 units.. Each unit requires 0.5 pound of cork. At the end of the current year, management expects to have 22,750 pounds of cork in inventory. Management has set a target to have cork on hand equal to one half of next month's sales requirements. Sales and production take place evenly throughout the year. Required: a. Compute the total targeted production of the finished coaster for the coming year. b. Compute the required amount of cork to be purchased for the coming year. amount of force exerted on an object due to gravity When the flow rate of a stream decreases,a. the largest dissolved materials are depositedb. the smallest dissolved materials are depositedc. the largest suspended materials are depositedd. the smallest suspended materials are deposited A ______ is the number of bits that can be accessed at one time by the CPU. bit rate. character. pulse width. word. Suppose a project requires an amount of C0 dollars today, but the project will generate a revenue of FV1 one year in the future, FV2 two years in the future, FV3 three years in the future, and so on for n years. If the interest rate is i, what is the net present value of the project? [From your textbook] Compute the following. d/dx (2xx+7x7) how to find confidence interval on ti 84 without standard deviation How is an understanding of the differences between American and Greek values useful to the study of modern American culture? Willie Company sells 36,000 units at $31 per unit, Variable costs are $20.15 per unit, and fixed costs are $175,800. Determine (a) the contribution margin ratio, (b) the unit contribution margin, and (c) operating income. a. Contribution margin ratio (Enter as a whole number.) b. Unit contribution margin (Round to the nearest cent.) % % c. Operating income