An angle (in radians) satisfies for

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

An angle θ(t)\theta(t) (in radians) satisfies tan⁡θ(t)=0.5t\tan \theta(t)=0.5t for t≥0t\ge 0. Define the function k(t)=sin⁡ ⁣(θ(t)2)k(t)=\sin\!\bigl(\theta(t)^{2}\bigr). Determine dkdt\dfrac{dk}{dt} at t=1t=1.

Related theory

Browse the problem library