Let be an angle in quadrant II such that sec(theta) -4/3 .

Question

Find the exact values of cot (theta) and sin (theta).

Answer 1

cos(theta)=1/sec(theta)= -3/4

sin(theta)+ OR - sqroot[1-cos^2(theta)]

Sine is positive in Quadrant II so:

sin(theta)=sqroot[1-(-3/4)^2]

sin(theta)=sqroot(1-9/16)

sin(theta)=sqroot(16/16-9/16)

sin(theta)=sqroot(7/16)

sin(theta = sqroot(7) / 4

cot(theta)=cos(theta)/sin(theta)

cot(theta)=(-3/4)/(sqroot(7)/4)

cot(theta)= -3/sqroot(7)