Question

If sin θ = 4/5, then find cos θ.

Answer 1

sin θ = 4/5 .. .(i)[Given] 

In right angled ∆ABC, ∠C = θ.

Let the common multiple be k. 

∴ AB = 4k and AC = 5k 

Now, AC² = AB² + BC² … [Pythagoras theorem] 

∴ (5k)² = (4k)² + BC² 

∴ 25k² = 16k² + BC² 

∴ BC² = 25k² – 16k² 

= 9k² 

∴ BC = √(9k²) .. .[Taking square root of both sides] 

= 3k