The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.

Solution:

Given, the point p(9, 12) is on the terminal side of θ.

We have to find the exact values of each trigonometric function.

Let r be the length of the line segment drawn from the origin to the point .

r = √x² + y²

Here, x = 9 and y = 12

r = √(9)² + (12)²

= √81 + 144

= √225

r = 15

sin θ = y/r = 12/15 = 4/5

cos θ =x/r = 9/15 = 3/5

tan θ = y/x = 12/9 = 4/3

cosec θ = 1/sin θ = 5/4

sec θ = 1/cos θ = 5/3

cot θ = 1/tan θ = 3/4 

Therefore, the exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3 and 3/4.

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The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.

Summary:

The point p(9, 12) lies on the terminal side of θ. The exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3 and 3/4.