   Chapter 8.2, Problem 8E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating Trigonometric Functions In Exercises 7–12, sketch a right triangle corresponding to the trigonometric function of the acute angle θ and find the values of the other five trigonometric functions of θ. cos   θ = 3 7

To determine

To calculate: The values of other five trigonometric functions of θ if cosθ=37.

Explanation

Given Information:

The value of trigonometric ratio is x is cosθ=37.

Formula used:

Circular function definition:

sinθ=yr         cscθ=rycosθ=xr         secθ=rxtanθ=yx         cotθ=xy

Where, x is the length of the side adjacent to θ, y is the length of the side opposite to θ, and r=x2+y2 is the length of hypotenuse which is not equal to 0.

Calculation:

From the provided trigonometric function, the value of x is 3 and r is 7. So, the value of y will be:

r=x2+y27=32+y27=9+y2

Take square both sides.

72=(9+y2)249=9+y2

Subtract 9 from both sides of the above equation.

49=9+y2499=9+y2940=y2y2=40

Now, take square root both sides.

y2=40y=210

Thus, y=210.

Use the obtained value of y and the provided value of x and r to create a right triangle corresponding to θ:

Now, substitute the value of x, y, and r to evaluate the exact value of the remaining trigonometric functions using circular function definition.

Now, for the value of sinθ.

sinθ=yr=2107

Now, for the value of cscθ

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