A-level · Trigonometry

Solving trigonometric equationsExam-style questions

The full method for solving trig equations in a range — quadratics in sin/cos, using sin²+cos²≡1 to convert a mixed equation, and transformed arguments like sin 2x and cos(x − 30°) where the interval must change.

Start practising Read the lesson

13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.
(a) Solve, for $0 < x < 2\pi$ , the equation

$4\sin^2 x - 3 = 5\cos x$

giving your answers in radians to 3 significant figures.

(5 marks)

On a summer's day, the temperature of the water in an outdoor swimming pool, $T\ ^\circ$ C, $t$ hours after midnight, is modelled by the equation

$T = 25 + 3.5\cos(kt + 80)^\circ \qquad 0 \leqslant t < 24$

where $k$ is a positive constant.

According to the model, the temperature of the water at 3 pm is $27.4\ ^\circ$ C.

Given that $k < 45$
(b) find, to 2 decimal places, each of the possible values of $k$ .

(4 marks)

Given further that $10 < k < 20$ , find, according to the model,
(c) the lowest temperature of the water during the day,

(1 mark)
(d) the time, to the nearest minute, at which the water is coldest.

(2 marks)
Level 5 · 12 marksTry it