Trigonometry

Learn

1. 1Radians, compound and double anglesRadians and arc length, the formulas for sin, cos and tan of A ± B, the double-angle formulas, and using them with ratios found from a right-angled triangle.Done20 min
2. 2Trigonometric equationsSolving trig equations for 0° to 360°: finding every solution from the quadrants, quadratic equations in sin or cos, and using the double-angle formulas to make one.Done18 min

Past questions (26)

From 2008–2023: 21 WAEC, 5 NECO. Theory questions first, then objective, newest first.

Theory (13)

• WAEC 2022 · Paper 2 · Q4Solve $3\cos2x - \sin x = 0$ for $0^\circ \le x \le 360^\circ$ (2 d.p.).
• WAEC 2022 · Paper 2 · Q4Solve, correct to the nearest degree, $3\cos^2\theta + 10\cos\theta - 8 = 0$, for $0^\circ \le \theta \le 360^\circ$.
• WAEC 2020 · Paper 2 · Q10If $15^y \times 5^{(2y - 2)} \times 9^{(y - 1)} = 1$, find the value of $y$.
• WAEC 2019 · Paper 2 · Q4If $\sin X = \dfrac{p - q}{p + q}$, where $0^\circ \le X \le 90^\circ$, find $1 - \tan^2 X$.
• WAEC 2019 · Paper 2 · Q10If $\sin p = \frac12$ and $\cos q = -\frac13$, evaluate $\sin(p - q)$, where $0^\circ \le p \le 90^\circ$ and $90^\circ \le q \le 180^\circ$.
• WAEC 2019 · Paper 2 · Q10The lengths of the sides of a triangle, in centimetres, are $(3 + \sqrt2)$, $2\sqrt3$ and $3\sqrt2$. Find the value of the largest angle of the …
• WAEC 2018 · Paper 2 · Q1If $\dfrac{\tan\theta + \tan30^\circ}{1 - \tan\theta\tan30^\circ} + 1 = 0$, find $\tan\theta$, leaving the answer in surd form.
• WAEC 2017 · Paper 2 · Q9Simplify $\dfrac{1}{1 - \cos\theta} + \dfrac{1}{1 + \cos\theta}$ and leave the answer in terms of $\sin\theta$.
• WAEC 2016 · Paper 2 · Q11If ${}^kP_2 = 72$, find the value of $k$.
• WAEC 2016 · Paper 2 · Q10Find the range of values of $x$ for which $3x^2 + x - 2 \le 0$.
• WAEC 2011 · Paper 2 · Q1Find the truth set of $\sin\theta + \cos2\theta = 0$, $0^\circ \le \theta \le 360^\circ$.
• WAEC 2009 · Paper 2 · Q4Given that $\tan 2A = \dfrac{2\tan A}{1 - \tan^2 A}$, evaluate $\tan 15^\circ$, leaving your answer in surd form.
• WAEC 2008 · Paper 2 · Q2If $\sin A = \frac35$ and $\cos B = \frac{15}{17}$, where $A$ is obtuse and $B$ is acute, find the value of $\cos(A + B)$.

Objective (13)

• NECO 2023 · Paper 1 · Q1Convert $45^\circ$ to radians in terms of $\pi$.
• NECO 2023 · Paper 1 · Q10In a circle of radius $20\text{ cm}$, find the length of an arc which subtends an angle of 1.2 radians at the centre.
• NECO 2023 · Paper 1 · Q11Given that $\cos A = \frac45$ and $\cos B = \frac{12}{13}$, find $\sin(A + B)$ if $A$ and $B$ are both acute.
• NECO 2023 · Paper 1 · Q14Solve $\sin^2x + 2\sin x + 1 = 0$ for $0^\circ < x < 360^\circ$.
• NECO 2023 · Paper 1 · Q21If $\sin\theta = \cos2\theta$ and $0^\circ < \theta < 90^\circ$, find the value of $4\theta$.
• WAEC 2023 · Paper 1 · Q25Solve $6\sin 2\theta \tan\theta = 4$, where $0^\circ < \theta < 90^\circ$.
• WAEC 2023 · Paper 1 · Q40Given that $\sin x = \frac{4}{5}$ and $\cos y = \frac{12}{13}$, where $x$ is an obtuse angle and $y$ is an acute angle, find the value of $\sin(x - y)$.
• WAEC 2023 · Paper 1 · Q9If $f: x \rightarrow 2\tan x$ and $g: x \rightarrow \sqrt{x^2 + 8}$, find $(g \circ f)(45^\circ)$.
• WAEC 2022 · Paper 1 · Q29Find, correct to the nearest degree, the acute angle formed by the lines $y = 2x + 5$ and $2y = x - 6$.
• WAEC 2022 · Paper 1 · Q30Solve: $4\sin^2\theta + 1 = 2$, where $0^\circ < \theta < 180^\circ$.
• WAEC 2022 · Paper 1 · Q7Express $\dfrac{4\pi}{5}$ radians in degrees.
• WAEC 2020 · Paper 1 · Q15If $\sin X = \frac{3}{5}$ and $\cos Y = \frac{24}{25}$, where $X$ and $Y$ are acute, find the value of $\cos(X + Y)$.
• WAEC 2020 · Paper 1 · Q3If $\cos x = -0.7133$, find the values of $x$ between $0^\circ$ and $360^\circ$.