Let, (-3,7) be a point on the terminal side of θ . Find the exact values of cos θ , csc θ , and tan θ .

Question

Let, (-3,7) be a point on the terminal side of θ . Find the exact values of cos θ , csc θ , and tan θ .

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the trig functions, cosθ, cscθ and tanθ. First, we must find out what r is using

r² = x² + y²

r = √x² + y² = √(-3)²+(7)² = √58

Then we use this plus the point (x,y) = (-3,7) to find these trig values. These values yield the form

cosθ = (x/r) = (-3/√58) = (-3√58 / 58)..............From rationalizing the denominator

cscθ = (r/y) = (√58 / 7)

tanθ = (y/x) = (-7/3)

I hope this helped!