The point P(-10, -2) is on the terminal side of an angle x. Find the exact values of each trigonometric function

Solution:

Given, the point p(-10, -2) 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 = -10 and y = -2

r = √(-10)² + (-2)²

= √100 + 4

r = √104

sin θ = y/r = -2/√104

cos θ = x/r = -10/√104

tan θ = y/x = -2/-10 = 1/5

cosec θ = 1/sin θ = -√104/2

sec θ = 1/cos θ = -√104/10

cot θ = 1/tan θ = 5

Therefore, the exact values of each trigonometric function are -2/√104, -10/√104, 1/5, -√104/2, -√104/10 and 5.

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The point P(-10, -2) is on the terminal side of an angle x. Find the exact values of each trigonometric function

Summary:

The point p(-10, -2) lies on the terminal side of θ. The exact values of each trigonometric function are -2/√104, -10/√104, 1/5, -√104/2, -√104/10 and 5.