Find the exact value of each of the remaining trigonometric functions of 0 cos0= - 3/4,0 in Quadrant II

Question

Find the exact value of each of the remaining trigonometric functions of 0

cos0= - 3/4,0 in Quadrant II

sin0 = ?

Answer 1

cos²x + sin²x = 1, Thus (-3/4)² + sin²x = 1

(9/16) + sin²x = 1

sin²x = 1 - (9/16) = (16/16) - (9/16) = (7/16)

sin x =±√(7/16) = ±(√7)/4

sin x = (√7)/4 sin sin x is positive in quadrant II

tan x = (sin x / cos x) = (√7/4) ÷ (-3/4) = (√7/4) × (-4/3) = (-√7)/(3)

Now sec x = (-4/3) sec x is the reciprocal of cos x

csc x = (4/√7) = (4√7)/(7) csc x is the reciprocal of sin x

cot x = (-3/√7) = (-3√7)/(7) cot x is the reciprocal of tan x