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Grade 10 Trigonometry — How to Identify the Question Type

Grade 10 trigonometry introduces sin, cos, and tan ratios in right-angled triangles, the special angle values (30°, 45°, 60°), and reading trigonometric functions from the unit circle. Identify whether a question gives you a triangle (use SOHCAHTOA) or an equation to solve.

Type 1: Using SOHCAHTOA to find a side or angle

Trigger words: "Calculate the value of x", "Find the length", "Determine the angle"

Trigger structure: A right-angled triangle is given (or can be constructed). Two measurements are known and one is unknown.

Do not confuse with: The sine rule or cosine rule — those apply to non-right-angled triangles and are Grade 11/12 content.

Method (no numbers — just the steps)

  1. Label the triangle: identify the right angle, the reference angle (θ), and the sides (opposite, adjacent, hypotenuse)
  2. Choose the correct ratio: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj
  3. Substitute the known values
  4. Solve for the unknown using algebra or the inverse trig function
Grade 10Paper 2Level 2 — Routine Procedures
6.1 In right-angled triangle ABC, B̂ = 90°, AB = 5, and AC = 13. Calculate the size of Â.

Source: DBE Mathematics Paper 2, November 2022, Question 6.1

Common mistake

Using sin when tan is needed — always identify opposite, adjacent, and hypotenuse relative to the given angle before choosing the ratio.

See the progression — same type, increasing difficulty

Easy
In a right-angled triangle, the angle is 30° and the hypotenuse is 10. Find the side opposite the 30° angle.

Practice question — not sourced from a past paper.

Medium
In right-angled triangle PQR, P̂ = 90°, QR = 15, and PR = 9. Calculate the size of Q̂.

Practice question — not sourced from a past paper.

Hard
A ladder 8 m long leans against a wall making an angle of 65° with the ground. Calculate how high up the wall the ladder reaches.

Practice question — not sourced from a past paper.

Type 2: Special angle values

Trigger words: "Without using a calculator", "Determine the exact value"

Trigger structure: The angle is 30°, 45°, or 60° (or 0° or 90°). The instruction 'without a calculator' signals that you must use known exact values.

Do not confuse with: Calculator questions — if a calculator is allowed and the angle is not special, just compute.

Method (no numbers — just the steps)

  1. Recall the special angle table: sin/cos/tan for 0°, 30°, 45°, 60°, 90°
  2. Substitute the exact values
  3. Simplify the expression — rationalize surds if needed
Grade 10Paper 2Level 2 — Routine Procedures
Without using a calculator, determine the exact value of: sin 60° × tan 30° + cos² 45°

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy
Without a calculator, find the value of sin 30° + cos 60°.

Practice question — not sourced from a past paper.

Medium
Without a calculator, simplify: tan 45° × cos 30°

Practice question — not sourced from a past paper.

Hard
Without a calculator, determine the exact value of: (sin 45° + cos 45°)²

Practice question — not sourced from a past paper.

Type 3: Solving a basic trig equation

Trigger words: "Solve for θ", "Find the value of θ if"

Trigger structure: A trigonometric ratio is set equal to a value and you must find the angle.

Do not confuse with: Finding a side — if a number (not an angle) is unknown, use SOHCAHTOA without inverse functions.

Method (no numbers — just the steps)

  1. Isolate the trig ratio: sin θ = value, cos θ = value, or tan θ = value
  2. Use the inverse function: θ = sin⁻¹(value) etc.
  3. At Grade 10, only the principal angle in [0° ; 360°] is required — check the quadrant for additional solutions if the interval is specified
Grade 10Paper 2Level 2 — Routine Procedures
Solve for θ: sin θ = 0.5, where 0° ≤ θ ≤ 90°

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy
Solve for θ: cos θ = 0, where 0° ≤ θ ≤ 360°

Practice question — not sourced from a past paper.

Medium
Solve for θ: tan θ = −1, where 0° ≤ θ ≤ 360°

Practice question — not sourced from a past paper.

Hard
Solve for θ: 2 sin θ − 1 = 0, where 0° ≤ θ ≤ 360°

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.