Angle θ is a principal angle that lies in quadrant 2 such that 0° ≤ θ ≤ 360°. Given each trigonometric ratio,

Question

i) determine the exact values of x,y, and r

ii) sketch angle θ in standard position

iii) determine the principal angle θ and the related acute angle B to the nearest degree

 

a) sin θ = 1/3

b) cot θ = -4/3

c) csc θ = 2.5

d) tan θ = -1.1

Answer 1

A)

 inverse sine (1/3) = 19.47 ----> 160.52877   x= sqrt(9-1) = sqrt(8) = 2*Sqrt(2); y = 1

 

 B) 

    tan T = -3/4 ---> inverse tangent (-3/4) = 36.87 ----> 143.13;   x=-3; y=4

 

C)sin T = 0.4

     T = inverse sine(0.4) = 23.57814 ----> 156.42182; y = 2; x = sqrt(25 - 4) = sqrt(21)

 

D) tan T = -1.1 ---> inverse tangent (-1.1) = 47.72 ---->  132.27;   1.1 = 11/10 ----> x=10 and y=11