Question

If q is between 0 and 90 degrees and tan theta=(7/8) find cos theta

Answer 1

Answer: see below

Explanation:

tan θ = 7/8

θ = tan^-1 (7/8) = 41.2 degrees

cos θ = 0.7526

Answer 2

`\tan\theta=\frac78`

Recall that

`1+\tan^2\theta=\sec^2\theta`

which means

`\sec^2\theta=(113)/(64)\implies\cos^2\theta=(64)/(113)`

Given that
`0^\circ<\theta<90^\circ`, we should expect
`\cos\theta>0`, so we when we take the square root, we assume a positive sign. Then

`\cos\theta=\sqrt{(64)/(113)}=\frac8{√(113)}`