Course NotesPracticePast Paper Archive

Trigonometry · Guided Practice

Trig Equations

14 questions with answers and video solutions. Try each one before revealing the answer.

1
Solve the equation cos x∘=0.5\displaystyle cos\ x^\circ = 0.5, for 0≤x<360.\displaystyle 0 \le x < 360.
2
Solve the equation cos x∘=−0.5\displaystyle cos\ x^\circ = -0.5, for 0≤x<360.\displaystyle 0 \le x < 360.
3
Solve the equation sin x∘=−0.4\displaystyle sin\ x^\circ = -0.4, for 0≤x<360.\displaystyle 0 \le x < 360.
4
Solve the equation tan x∘=5\displaystyle tan\ x^\circ = 5, for 0≤x<360.\displaystyle 0 \le x < 360.
5
Solve the equation 9 tan x∘−1=6\displaystyle 9\ tan\ x^\circ - 1 = 6, for 0≤x<360.\displaystyle 0 \le x < 360.
6
Solve the equation 3 sin x∘+5=4\displaystyle 3\ sin\ x^\circ + 5 = 4, for 0≤x<360.\displaystyle 0 \le x < 360.
7
Write the following in order of size, starting with the smallest.

sin 200∘\displaystyle sin\ 200^\circ, sin 160∘\displaystyle sin\ 160^\circ, sin 180∘\displaystyle sin\ 180^\circ

Justify your answer.
8
2014 P2 Q12
3 Marks

Solve the equation 11cos⁡x∘−2=3\displaystyle 11\cos x^\circ - 2 = 3, for 0≤x≤360.\displaystyle 0 \le x \le 360.

9
2016 P2 Q14
3 Marks

Solve the equation 2tan⁡x∘+5=−4\displaystyle 2\tan x^{\circ}+5=-4, for 0≤x≤360\displaystyle 0\le x\le360.

10
2018 P2 Q8
3 Marks

Solve the equation 7sin⁡x∘+2=3\displaystyle 7\sin x^{\circ}+2=3, for 0≤x<360.\displaystyle 0\le x < 360.

11
2019 P2 Q14
3 Marks

Solve the equation 5cos⁡x∘+2=1\displaystyle 5\cos x^{\circ}+2=1, for 0≤x<360.\displaystyle 0\le x<360.

12
2022 P2 Q9
3 Marks

Solve the equation 3sin⁡x∘+4=6\displaystyle 3\sin x^{\circ}+4=6, for 0≤x≤360\displaystyle 0 \le x \le 360.

13
2024 P2 Q11
3 Marks

Solve the equation 17sin⁡x∘+1=9\displaystyle 17 \sin x^{\circ} + 1 = 9, for 0≤x<360.\displaystyle 0 \le x < 360.

14
2026 P2 Q8
3 Marks
Solve the equation
5tan⁡x∘+3=4\displaystyle 5\tan x^{\circ}+3=4, for 0≤x<360.\displaystyle 0\le x\lt360.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

All practice topics