Trigonometry Identities

Question

Given that cot m=0.75 and cos m<0, what is the value of sin m?

Answer 1

a^2+b^2=c^2

cot A = a/b = 0.75 > 0 ( Q1 or Q3)

cos A < 0 (Q2 or Q3)

sin A = b/c

a^2/b^2+1=c^2/b^2

cot^2 A + 1 = 1 / sin^2 A

sin^2 A = 1 / (cot^2 A + 1) = 1 / (0.75^2 + 1) = 0.64

sin A = +sqrt(0.64) = 0.8 (Q1 or Q2)

sin A = -sqrt(0.64) = -0.8 (Q3 or Q4)

Pick -0.8 from Q3 as the answer