# How do you use differentials to estimate the value of #cos(63)#?

Approximating by differential = linear approximation = use the tangent line at a nearby point.

At some point, either before we begin or within the functions we use, we'll have to change to radian measure. (Really we change to numbers.

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You can use differentials to estimate the value of ( \cos(63^\circ) ) by considering a small change in the angle, let's say ( d\theta ), and approximating ( \cos(63^\circ) ) as ( \cos(60^\circ + d\theta) ) since ( 63^\circ = 60^\circ + 3^\circ ). Then, you can use the differential ( d\cos(\theta) = -\sin(\theta) , d\theta ) to estimate ( \cos(63^\circ) ) based on the value of ( \sin(60^\circ) ).

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