Question

If `sin θ = 3/5` and θ is an acute angle, find (i) cos θ, (ii) tan θ.

Answer 1

Given: `sin θ = 3/5`, θ is acute.

Step-wise calculation:

1. Use identity sin²θ + cos²θ = 1.

2. `cos^2θ = 1 - (3/5)^2`

= `1 - 9/25`

= `16/25`

3. θ is acute

⇒ cos θ > 0

So, `cos θ = sqrt(16/25)`

= `4/5`

4. `tan θ = (sin θ)/(cos θ)` 

= `(3/5)/(4/5)`

= `3/4`

i. `cos θ = 4/5`

ii. `tan θ = 3/4`