Mastering Advanced Trigonometry Concepts Quiz

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Questions and Answers

What is the value of $d(PQ)$?

$2 - 2\cos(A-B)$ (correct)
$\sqrt{2 - 2\cos(A-B)}$
$1 + 1 - 2\cos(A-B)$
$\sqrt{1 + 1 - 2\cos(A-B)}$

What is the value of $\tan(\theta + \frac{\pi}{2})$?

$\cot\theta$
$\frac{\sin(\theta + \frac{\pi}{2})}{\cos(\theta + \frac{\pi}{2})}$
$-\cot\theta$ (correct)
$-\frac{\pi\cos(\theta + \frac{\pi}{2})}{2\sin(\theta + \frac{\pi}{2})}$

What is the value of $\tan(-\theta)$?

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

What is the value of $\cos(A+B)$?

$\cos A\cos B - \sin A\sin B$ (D) Signup and view all the answers

What is the value of $\sin(-\theta)$?

$-\sin\theta$ (C) Signup and view all the answers

What is the expansion of $cos(2(A-B))$?

$cos(2(A-B)) = cos^2(A-B) - sin^2(A-B) Signup and view all the answers

Using the given theorem, prove that $sin(-\theta) = -sin(\theta)$.

Using the identity $sin(-\theta) = -sin(\theta)$, we can rewrite it as $sin(-\theta) = -sin(\theta)$. Therefore, $sin(-\theta) = -sin(\theta) Signup and view all the answers

Explain the relationship between $tan(-\theta)$ and $cot(\theta)$ using the given theorem.

The relationship between $tan(-\theta)$ and $cot(\theta)$ is given by the identity $tan(-\theta) = -cot(\theta)$. Therefore, $tan(-\theta) = -cot(\theta) Signup and view all the answers

Prove that $cos(A+B) = cos(A)cos(B) - sin(A)sin(B)$ using the given theorem.

Using the identity $cos(A+B) = cos(A)cos(B) - sin(A)sin(B)$, we can rewrite it as $cos(A+B) = cos(A)cos(B) - sin(A)sin(B)$. Therefore, $cos(A+B) = cos(A)cos(B) - sin(A)sin(B) Signup and view all the answers