Question

sinθ + cosθ = ______.

Options

• 1

• `1 2/5`

• 2

• 3

Answer 1

sinθ + cosθ = `underlinebb(1 2/5)`.

Explanation:

Right triangle with hypotenuse 12 and other side 9 ⇒ third side 

= `sqrt (12^2 − 9^2) = 3sqrt7`

So sin⁡ θ ⁡ = `9/12 = 3/4`

cos θ = `(3sqrt7)/12 = sqrt7/4`

sin θ + cos θ = `(3 + sqrt7)/4 ≈ 1.41 = 1 2/5`