Last updated on Oct 10, 2026

Derivatives of Circular Functions (VCE SSCE Mathematical Methods): Quizzes

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Derivatives of Circular Functions

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What is the derivative of $\sin(k\theta)$ with respect to $\theta$ ?

$k\cos(k\theta)$

What is the derivative of $\cos(k\theta)$ with respect to $\theta$ ?

$-k\sin(k\theta)$

What is the derivative of $\tan(k\theta)$ with respect to $\theta$ ?

$k\sec^2(k\theta)$

What is the value of $\lim_{\theta \to 0} \frac{\sin \theta}{\theta}$ ?

$1$

How is the secant function $\sec \theta$ defined?

$\frac{1}{\cos \theta}$

What is $\frac{d}{d\theta}[\sin^2(2\theta)]$ ?

$4\sin(2\theta)\cos(2\theta)$

What is $\frac{d}{d\theta}[\cos^3(4\theta+1)]$ ?

$-12\cos^2(4\theta+1)\sin(4\theta+1)$

What is $\frac{d}{d\theta}[\tan(3\theta^2+1)]$ ?

$6\theta \sec^2(3\theta^2+1)$

Which complementary angle identity is correct?

$\cos \theta = \sin(\frac{\pi}{2}-\theta)$

For $y = \tan \theta$ , what is the gradient at $\theta = \frac{\pi}{4}$ ?

$2$

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