Take this Exam: Higher Maths: trigonometry | Zestly

Question 1

Solve $2\cos x^\circ + 1 = 0$ for $0 \leq x \leq 360$.

Accepted Answer

$x = 120$ and $x = 240$

Answer

$x = 60$ and $x = 300$

Answer

$x = 60$ and $x = 120$

Answer

$x = 240$ and $x = 300$

Question 2

Express $3\cos x^\circ + 4\sin x^\circ$ in the form $k\cos(x - a)^\circ$, where $k > 0$ and $0 \leq a \leq 360$. Give $a$ to one decimal place.

Accepted Answer

$5\cos(x - 53.1)^\circ$

Answer

$7\cos(x - 53.1)^\circ$

Answer

$5\cos(x + 53.1)^\circ$

Answer

$5\cos(x - 36.9)^\circ$

Question 3

What are the maximum and minimum values of $y = 3\sin(2x) + 1$?

Accepted Answer

maximum 4, minimum $-2$

Answer

maximum 3, minimum $-3$

Answer

maximum 4, minimum $-4$

Answer

maximum 6, minimum $-6$

Question 4

What is the exact value of $\cos 75^\circ$, using the fact that $75^\circ = 45^\circ + 30^\circ$?

Answer

$\frac{\sqrt{2} - \sqrt{6}}{4}$

Answer

$\frac{\sqrt{3} - 1}{2}$

Answer

$\frac{\sqrt{6} - \sqrt{2}}{4}$

Answer

$\frac{\sqrt{6} + \sqrt{2}}{4}$

Question 5

What is the period, in degrees, of the graph of $y = 5\cos(3x)$?

Answer

$60^\circ$

Answer

$120^\circ$

Answer

$360^\circ$

Answer

$1080^\circ$