TMUA · Paper 1: Applications of Mathematical Knowledge

Trigonometry

22 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 22 questions

The angle $θ$ is acute and $sin θ = \frac{3}{5}$ . What is the value of $sin 2 θ$ , where $sin 2 θ = 2 sin θ cos θ$ ?
How many solutions does $2 sin^{2} x - sin x - 1 = 0$ have in the interval $0 \leq x < 2 π$ ?
How many solutions does $sin x = \frac{1}{3}$ have in the interval $0 \leq x \leq 4 π$ ?
It is given that $sin x + cos x = \frac{1}{2}$ . What is the value of $sin x cos x$ ?
What is the minimum value of $5 sin^{2} x + 2 cos^{2} x$ for real $x$ ?
It is given that $tan x = 2$ and $x$ is acute. What is $sin^{2} x$ ?
A triangle has two sides of lengths $5$ and $8$ with an angle of $3 0^{\circ}$ between them. What is its area?
A triangle has sides of length $3$ , $5$ and $7$ . What is the size of its largest angle, in degrees?
In triangle $A B C$ , side $a = 10$ is opposite angle $A = 3 0^{\circ}$ and $B = 4 5^{\circ}$ . What is the length of side $b$ , opposite angle $B$ ?
A sector of a circle has radius $6$ and angle $\frac{2 π}{3}$ radians. What is its area?
What is the exact value of $cos \frac{5 π}{6}$ ?
How many solutions does $sin 2 x = \frac{1}{2}$ have in the interval $0 \leq x \leq 2 π$ ?
The curve $y = 3 cos 2 x + 1$ has its smallest positive $x$ -coordinate minimum at $x = p$ . What is $p$ ?
How many solutions does $tan x = 2 sin x$ have in the interval $0 \leq x < 2 π$ ?
What is the sum of all the solutions of $cos^{2} x - sin^{2} x = \frac{1}{2}$ in the interval $0 \leq x \leq π$ ?
The angle $θ$ is obtuse and $cos θ = - \frac{1}{3}$ . What is $tan θ$ ?
For $cos x \neq = 1$ , the expression $\frac{sin ^{2} x}{1 - cos x}$ simplifies to $1 + cos x$ . What is its value when $cos x = \frac{1}{4}$ ?
The sides of a triangle are $13$ , $14$ and $15$ . What is its area?
What is the sum of the solutions of $sin x = - \frac{3}{2}$ in the interval $0 \leq x \leq 2 π$ ?
What is the exact value of $tan \frac{π}{3} \times cos \frac{π}{6}$ ?
How many solutions does $cos x = cos 3 x$ have in the interval $0 \leq x \leq 2 π$ ?
What is the number of solutions of $2 cos^{2} x + 3 sin x = 3$ in the interval $0 \leq x \leq 2 π$ ?

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