Question

Note: Triangle may not be drawn to scale. Suppose a = 80 and b = 39 . Find an exact value. (Write a fraction.)

Answer 1

The exact values of the given trigonometric functions are

$sin(A) = \frac{80}{89}$

$cos(A) = \frac{39}{89}$

$tan(A) = \frac{80}{39}$

$sec(A) =\frac{89}{39}$

$csc(A) =\frac{89}{80}$

$cot(A) =\frac{39}{80}$

Trigonometry

From the question, we are to determine the values of the trigonometric functions

First, we will determine the length of side c

By the Pythagorean theorem, we have that

c² = a² + b²

c² = 80² + 39²

c² = 6400 + 1521

c² = 7921

c = √7921

c = 89

Now, Using SOH CAH TOA

That is,

$sin(A) = \frac{opposite}{hypotenuse}$

$cos(A) = \frac{adjacent}{hypotenuse}$

$tan(A) = \frac{opposite}{adjacent}$

In the triangle,

opposite = a = 80

adjacent = b = 39

hypotenuse = c = 89

Thus,

$sin(A) = \frac{80}{89}$

$cos(A) = \frac{39}{89}$

$tan(A) = \frac{80}{39}$

$sec(A) =\frac{1}{cos(A)} =\frac{89}{39}$

$csc(A) =\frac{1}{sin(A)} =\frac{89}{80}$

$cot(A) =\frac{1}{tan(A)} =\frac{39}{80}$

Hence, the exact values of the given trigonometric functions are

$sin(A) = \frac{80}{89}$

$cos(A) = \frac{39}{89}$

$tan(A) = \frac{80}{39}$

$sec(A) =\frac{89}{39}$

$csc(A) =\frac{89}{80}$

$cot(A) =\frac{39}{80}$

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