Singapore GCE O-Level · Additional Mathematics

Trigonometric Functions, Identities and Equations

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

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Express $3 cos θ - 4 sin θ$ in the form $R cos (θ + α)$ , where $R > 0$ and $0^{\circ} < α < 9 0^{\circ}$ .
Solve the trigonometric equation $2 cos (2 x) = 1$ for $0 \leq x \leq π$ .
Simplify the trigonometric expression: $\frac{s i n ( 2 θ )}{1 + c o s ( 2 θ )}$ .
Given that $tan A = \frac{1}{2}$ and $tan B = \frac{1}{3}$ , find the exact value of the acute angle $(A + B)$ .
Find the maximum and minimum values of the function $f (θ) = 8 - 3 sin (2 θ - \frac{π}{4})$ .
Solve for $θ \in [0, 2 π]$ : $4 sin^{2} θ + 8 cos θ - 7 = 0$ .
Find the exact value of $sin 3 0^{\circ}$ .
Find the exact value of $cos 3 0^{\circ}$ .
Find the exact value of $tan 3 0^{\circ}$ .
Find the exact value of $sin 6 0^{\circ}$ .
Find the exact value of $cos 6 0^{\circ}$ .
Find the exact value of $tan 6 0^{\circ}$ .
Given that $sin θ = \frac{5}{13}$ and $θ$ is acute, find the value of $tan θ$ .
Given that $sin θ = \frac{3}{5}$ and $θ$ is acute, find the value of $tan θ$ .
Given that $sin θ = \frac{8}{17}$ and $θ$ is acute, find the value of $tan θ$ .
Given that $sin θ = \frac{7}{25}$ and $θ$ is acute, find the value of $tan θ$ .
Given that $sin θ = \frac{20}{29}$ and $θ$ is acute, find the value of $tan θ$ .
Find the maximum value of $3 sin x + 4 cos x$ .
Find the maximum value of $5 sin x + 12 cos x$ .
Find the maximum value of $4 sin x + 3 cos x$ .
Solve $2 sin x = 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $2 cos x = 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $2 sin x = 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $2 sin x = 3$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $2 cos x = - 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $tan x = 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $tan x = 3$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
Solve $2 cos x = - 1$ for $0^{\circ} \leq x \leq 36 0^{\circ}$ .
State the amplitude and the period of $y = 3 sin 2 x + 1$ .
State the amplitude and the period of $y = 2 sin 4 x - 1$ .
State the amplitude and the period of $y = 5 sin 3 x + 2$ .
State the amplitude and the period of $y = 4 sin 6 x$ .
Simplify $sin^{2} x + cos^{2} x$ .
Simplify $\frac{s i n x}{c o s x}$ .
Simplify $1 + tan^{2} x$ .
Simplify $1 + cot^{2} x$ .
Simplify $2 sin x cos x$ .
Simplify $cos^{2} x - sin^{2} x$ .
Convert $3 0^{\circ}$ to radians.
Convert $4 5^{\circ}$ to radians.
Convert $6 0^{\circ}$ to radians.
Convert $9 0^{\circ}$ to radians.
Convert $12 0^{\circ}$ to radians.
Convert $15 0^{\circ}$ to radians.
Convert $13 5^{\circ}$ to radians.
Convert $27 0^{\circ}$ to radians.
A sector of a circle of radius $6$ cm subtends an angle of $2$ radians at the centre. Find the area of the sector.
A sector of a circle of radius $10$ cm subtends an angle of $1$ radians at the centre. Find the area of the sector.
A sector of a circle of radius $8$ cm subtends an angle of $3$ radians at the centre. Find the area of the sector.
A sector of a circle of radius $5$ cm subtends an angle of $2$ radians at the centre. Find the area of the sector.
A sector of a circle of radius $12$ cm subtends an angle of $1$ radians at the centre. Find the area of the sector.

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Trigonometric Functions, Identities and Equations

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