Question

let (-5,-7) be a point on the terminal side of theta. find the exact values of cos theta, sec theta, and cot theta

Answer 1

a. The exact value of cosθ = -5/√74

b. The exact value of secθ = -√74/5

c. The exact value of cotθ = 5/7

How to find the trigonometric ratios

Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.

So, r = √(x² + y²) where

• x = -5 and
• y = -7

So, r = √(x² + y²)

r = √((-5)² + (-7)²)

r = √(25 + 49)

r = √74

The value of the trigonometric ratio cosθ

Since the trigonometric ratio cosθ = x/r

Substituting the values of x and r into the equation, we have

cosθ = x/r

cosθ = -5/√74

So, the exact value of cosθ = -5/√74

The value of the trigonometric ratio secθ

Since the trigonometric ratio, secθ = r/x

Substituting the values of x and r into the equation, we have

secθ = r/x

secθ = √74/-5

secθ = -√74/5

So,  the exact value of secθ = -√74/5

The value of the trigonometric ratio cotθ

Since the trigonometric ratio cotθ = x/y

Substituting the values of x and y into the equation, we have

cotθ = x/y

cotθ = -5/-7

cotθ = 5/7

So,  the exact value of cotθ = 5/7

Learn more about trigonometric ratios here:

brainly.com/question/1518222

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