Trigonometry?

Question

if tanθ = √63 and cos θ is negative, find sin θ .

Answer 1

Tangent formula, tanθ = sinθ / cosθ

∴ sinθ = tanθ * cosθ

sinθ = tanθ / secθ                      [Since cosθ = 1/secθ]

Squaring on both sides we get,

sin²θ = tan²θ / sec²θ

 = tan²θ / (1 + tan²θ)                 [Since sec²θ = 1 + tan²θ]

= (√63)² / (1 + (√63)²)               [Since tanθ = √63]

= 63 / (1 + 63)

= 63 / 64

cosθ is negative and tanθ is positive, hence θ lies in third quadrant where sinθ is negative.

So, sinθ = - √(63/64)

= - √(63) / √(64)

= -√(63) / 8