# Let (−4,5) Be A Point On The Terminal Side Of θ . Find The Exact Values Of Cosθ , Secθ , And Cotθ?

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## Let (−4,5) be a point on the terminal side of θ . Find the exact values of cosθ , secθ , and cotθ?

Learn the general definitions. With any (x,y) on the terminal side, define:

r = √(x² + y²)

…and then the functions of θ (measured counter-clockwise from the +x axis) are:

cos θ = x/r …. sec θ = r/x

sin θ = y/r …. csc θ = r/y

tan θ = y/x …. cot θ = x/y

For your problem, r = √[(-4)² + 5²] = √(16 + 25) = √41, and all the ratios follow.

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