Question

Find theta if theta is between 0 degrees and 90 degrees and tan theta = 7/8, find cos theta

Answer 1

Answer: see below

Explanation:

Presuming you meant this

0< θ < 90 degree; tan (θ) = 7/8 find cos (θ)

Using the identity

1 + tan²θ = sec²θ (where sec θ = 1/cosθ)

cosθ = √{1/(1 + tan²θ)} = √{ 1/(1 + (7/8)²} = √{ 1/(1 + 49/64)}

= √{ 64/113} = 8/√113 <= answer.

Answer 2

tan θ = 7/8
θ = tan^-1 (7/8) = 41.2 degrees

cos θ = 0.7526