Answer :

cos 61°, it being given that sin 60° = 0.86603 and 1° = 0.01745 radian


Let us assume that f(x) = cos x


Also, let x = 60° so that x + Δx = 61°


60° + Δx = 61°


Δx = 1° = 0.01745 radian


On differentiating f(x) with respect to x, we get



We know



When x = 60°, we have



Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 0.01745


Δf = (–0.86603)(0.01745)


Δf = –0.0151122


Now, we have f(61°) = f(60°) + Δf


f(61°) = cos(60°) – 0.0151122


f(61°) = 0.5 – 0.0151122


f(61°) = 0.4848878


Thus, cos 61° ≈ 0.4848878


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