Question

If sin θ = 0.6, find sec θ + tan θ.

Answer 1

Given:

sin θ = 0.6 = `3/5​`

In a right triangle, if sin ⁡θ = `3/5` then:

Opposite side = 3θ

Hypotenuse = 5θ

adjacent side = `sqrt((5θ)^2 − (3θ)^2) = sqrt (25θ^2 − 9θ^2) = 4θ`

`cos θ = 4/5, sec θ = 5/4`

tan θ = `"opposite"/"adjacent" = 3/4`

sec θ + tan θ = `5/4 + 3/4 = 8/4`

sec θ + tan θ = 2