Question

Find sin(90° - θ), cos θ and tan θ.

Answer 1

Given:

QR = 12 units (adjacent to angle θ)

PR = 15 units (hypotenuse)

∠Q = 90°

∠P = θ

We need to find:

sin (90° − θ)

cos θ

tan θ

Step 1: Find the third side (PQ)

Use the Pythagoras Theorem:

QR² = PR² − PQ²

= 12² − 15² = 225

= 225 − 144 = 81

⇒ PQ = `sqrt81` = 9

QR = 12 (opposite to θ)

PQ = 9 (adjacent to θ)

PR = 15 (hypotenuse)

Step 2: Apply trigonometric ratios

`cos θ = "adjacent"/"hypotenuse" = (PQ)/(PR) = 9/15 = 3/5`

sin (90° − θ) = `3/5`

`cos θ = "adjacent"/"hypotenuse" = (PQ)/(PR) = 9/15 = 3/5`

`tan θ = "opposite"/"adjacent" = (QR)/(PQ) = 12/9 = 4/3`