Question

Given cos(α) = √32/9 and 0 < α < π/2, find the exact values of the remaining five trigonometric functions. 

Answer 1

Solution

given cos(a)=√32/9 and 0

Since cosa=base/hypotenuse

so, base=√32 and hypotenuse=9

using Pythagoras theorem

(Hypotenuse)^2=(base)^2+(perpendicular)^2

(Perpendicular)^2=(hypotenuse)^2-(base)^2

(Perpendicular)^2=9^2-(√32)^2

(Perpendicular)^2=81-32

(Perpendicular)^2=49

perpendicular=√49=7

now , sin(a)=perpendicular/hypotenuse=7/9

Csc(a)=1/sin(a)=9/7

sec(a)=1/cosa=9/√32

tan(a)=perpendicular/base=7/√32

cot(a)=1/tan(a)=√32/7

and these all are positive because (a) is in first quadrant.