Question bank

TMUA-P1-MM4-001

What is the exact value of $\cos 60^\circ$?

TMUA-P1-MM4-002

Convert $60^\circ$ to radians, giving your answer as a multiple of $\pi$.

TMUA-P1-MM4-003

In triangle $ABC$, angle $A = 30^\circ$, angle $B = 90^\circ$ and side $a = 5$. What is the length of side $b$?

TMUA-P1-MM4-004

A triangle has sides of length $6$ and $8$ with included angle $90^\circ$. What is its area?

TMUA-P1-MM4-005

A triangle has sides of length $5$ and $7$ with included angle $60^\circ$. What is the length of the third side?

TMUA-P1-MM4-006

Find all values of $\theta$ with $0 \le \theta < 360^\circ$ satisfying $2\sin\theta - 1 = 0$.

TMUA-P1-MM4-007

A circle has radius $6$. What is the length of the arc subtending an angle of $\frac{2\pi}{3}$ radians at the centre?

TMUA-P1-MM4-008

A sector of a circle of radius $4$ has angle $\frac{3\pi}{4}$ radians. What is its area?

TMUA-P1-MM4-009

The angle $\theta$ is acute and $\sin\theta = \frac{5}{13}$. What is the value of $\cos\theta$?

TMUA-P1-MM4-010

What is the maximum value of $y = 3 - 2\sin x$?

TMUA-P1-MM4-011

A triangle has sides of length $4$, $5$ and $6$. What is the cosine of its largest angle?

TMUA-P1-MM4-012

The equation $2\sin^2 x = 1$ has four solutions in $0 \le x < 2\pi$. What is their sum?

TMUA-P1-MM4-013

What is the exact value of $\sin 30^\circ$?

TMUA-P1-MM4-014

Solve $\sin x = \frac{\sqrt{3}}{2}$ for $0^\circ < x < 90^\circ$.

TMUA-P1-MM4-015

What is the exact value of $\cos 45^\circ$?

TMUA-P1-MM4-016

If $\sin\theta = \frac{3}{5}$ with $\theta$ acute, find $\cos\theta$.

TMUA-P1-MM4-017

What is the maximum value of $3\sin(2x)$?

TMUA-P1-MM4-018

How many solutions does $2\sin^2 x - \sin x - 1 = 0$ have for $0^\circ \leq x < 360^\circ$?

TMUA-P1-MM4-019

Solve $\cos x = -\frac{1}{2}$ for $0^\circ < x < 360^\circ$.

TMUA-P2-MM4-001

How many integers $x$ satisfy $|2x - 3| < 5$?