Let y=sinθ . If percentage error in measuring angle at θ=π/4 is 2% then the percentage error in y at that angle is

Given:
y = sinθ
θ = π/4
Percentage error in θ = 2%

We need to determine the percentage error in y at θ = π/4.

Step 1: Use Differential Method
The error in y can be approximated using differentiation:

dy/dθ = cosθ

Using the concept of percentage error:
Percentage error in y = (dy/y) × 100

Using dy = (dy/dθ) dθ, we get:
dy/y = (cosθ / sinθ) dθ

So,
Percentage error in y = (cosθ / sinθ) × Percentage error in θ

Step 2: Substitute Given Values
At θ = π/4:
sin(π/4) = 1/√2
cos(π/4) = 1/√2

Thus,
Percentage error in y = ( (1/√2) / (1/√2) ) × 2%
= 1 × 2%
= 2%

Final Answer
The percentage error in y at θ = π/4 is 2%.