Question

If 1° = 0.01745 then, what is the value of cos62°?

(a) 0.4588

(b) 0.4788

(c) 0.4688

(d) 0.3688

I got this question by my college professor while I was bunking the class.

My question is based upon Application of Derivative for Error Determination topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (c) 0.4688

Explanation: Let, y = f(x) = cosx

And, x = 60° = π/3, δx = 2° = 2 * 0.01745 = 0.03490

Since f(x) = cosx, hence

f’(x) = -sinx

Now, we have f(x + δx) = f(x) + f’(x) δx

Or, f(60° + 2°) = f(60°) + f’(60°) * 0.0349

Or, f(62°) = cos(60°) – sin60° * 0.0349

Or, cos62° = 0.5 – 0.866 * 0.0349 = 0.4688