Trigonometry — Practice

Question 1

State the three square-relation identities.

Accepted Answer

sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

Question 2

If sin θ = 3/5, find cos θ.

Accepted Answer

cos²θ = 1 − 9/25 = 16/25 → cos θ = 4/5.

Question 3

A ladder makes 60° with the ground and reaches 6 m up a wall. Find the ladder's length.

Accepted Answer

sin60° = 6/L → √3/2 = 6/L → L = 12/√3 = 4√3 m.

Question 4

If tan θ = 3/4, find sec θ.

Accepted Answer

sec²θ = 1 + 9/16 = 25/16 → sec θ = 5/4.

Question 5

A tower subtends 45° elevation from a point 20 m away. Find its height.

Accepted Answer

tan45° = h/20 → h = 20 m.

Question 6

Define the angle of depression.

Accepted Answer

The angle below the horizontal when an observer looks down at an object.

Practice — Trigonometry