Practice Maths

Topic Review — Trigonometric Functions

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★ U1T4 — Trigonometric Functions Review

Covers: Radian measure • Arcs & sectors • Exact values • Trig graphs • Transformations • Solving equations

  1. Q1 — Radian conversion

    Convert each angle to radians (exact): (a) 60°   (b) 270°   (c) 135°   (d) 210°

  2. Q2 — Radian to degrees

    Convert to degrees: (a) π/4   (b) 5π/6   (c) 4π/3   (d) 11π/6

  3. Q3 — Arc length and sector area

    A sector has radius 8 cm and angle 5π/6 radians. Find: (a) arc length   (b) sector area.

  4. Q4 — Exact values

    Evaluate exactly: (a) sin(π/6)   (b) cos(2π/3)   (c) tan(π/4)   (d) sin(5π/4)   (e) cos(11π/6)

  5. Q5 — Period and amplitude

    State the amplitude and period of: (a) y = 5cos(3x)   (b) y = −2sin(x/2)   (c) y = 4tan(2x)

  6. Q6 — Key features of a transformed function

    For y = 3sin(2x − π/3) + 2, state the amplitude, period, phase shift, vertical shift, maximum and minimum values.

  7. Q7 — Solving basic equations

    Solve for x ∈ [0, 2π]: (a) cos(x) = √3/2   (b) tan(x) = −√3   (c) 2sin(x) + 1 = 0

  8. Q8 — Equations with double angle

    Solve sin(2x) = √3/2 for x ∈ [0, 2π].

  9. Q9 — Find the equation from features

    A sine function has amplitude 4, period 3π, midline y = −1, and phase shift π/4 to the right. Write its equation.

  10. Q10 — Application: sprinkler

    A rotating sprinkler waters a circular region. The water reaches 5 m. The sprinkler turns through an angle of 2π/3 radians. Find: (a) the arc length of the watered edge   (b) the area of the sector watered.

  11. Q11 — Application: daylight hours model

    The number of daylight hours in Brisbane is modelled by D = 1.5sin(2π(t − 81)/365) + 12.1, where t is the day of the year. Find: (a) the maximum and minimum daylight hours   (b) the day of maximum daylight   (c) when daylight hours equal 12.

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