Let , (5−2) be a point on the terminal side of θ .Find the exact values of cosθ , cscθ , and tanθ

Answer 1

(5,-2) is in the 4th quadrant where cosines are always >0, tangents<0 and cosecants<0

using the Pythagorean theorem, the hypotenuse squared = 5^2 + (-2)^2 = 29

hypotentuse = sqr(29), adjacent side =5, opposite side = -2

cosT = adjacent side over hypotenuse = 5/sqr(29)

tanT = opposite side over adjacent side = -2/5 = -0.4

cscT = 1/sinT = 1/(opposite side/hypotenuse)

= hypotenuse/opposite side = sqr(29)/-2 = -sqr(29)/2

(using T = Theta)