a. The exact value of cosθ = -5/√74
b. The exact value of secθ = -√74/5
c. The exact value of cotθ = 5/7
<h3>How to find the trigonometric ratios</h3>
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
So, r = √(x² + y²)
r = √((-5)² + (-7)²)
r = √(25 + 49)
r = √74
<h3>The value of the trigonometric ratio cosθ</h3>
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
<h3>The value of the trigonometric ratio secθ</h3>
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
<h3>The value of the trigonometric ratio cotθ</h3>
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:
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