Trigonometry Questions and Answers

In triangle $ABC$ the sides $BC$, $CA$ and $AB$ are $a$, $b$ and $c$ respectively, and $\cot C = \dfrac{a}{c}\operatorname{cosec} B - \cot B$. Given $a = 14.7$ cm, $c = 17.3$ cm and $B = 64.2°$, find angle $C$ correct to the nearest $0.1°$.

In triangle $ABC$, $a = 14.7$ cm, $c = 17.3$ cm, $B = 64.2°$ and $C = 65.3°$. Find angle $A$ correct to the nearest $0.1°$.

In triangle $ABC$, $AB = m$ cm, $AC = 12$ cm and angle $B\hat{A}C = 60°$. Given that the area of the triangle is $\sqrt{675}$ cm$^2$, find the exact value of $m$.

Given $f(x)=\dfrac{2x-3}{x^2}$, differentiate from first principles to find $f'(x)$.

For $f(x)=\dfrac{2x-3}{x^2}$, with $f'(x)=\dfrac{-2x+6}{x^3}$, find the equation of the tangent to the curve at $x=2$.

Express $2\cos\theta-\sqrt3\sin\theta$ in the form $R\sin(\theta-\alpha)$, with $R>0$ and $0^\circ<\alpha<360^\circ$.

In a triangle ABC, $\hat{BAC}=\left(\dfrac{\pi}{2}+\theta\right)$ radians and $\hat{ACB}=\left(\theta-\dfrac{\pi}{2}\right)$ radians. Find $\hat{ABC}$ in radians.

Angles $A$ and $B$ satisfy $A + B = 45^\circ$, and it follows that $\tan A + \tan B + \tan A\tan B = 1$. By putting $A = B = 22\tfrac12^\circ$ and writing $t = \tan 22\tfrac12^\circ$, write down the resulting quadratic equation in $t$.