Worked example 1
Solve a sine equation
Solve 2sin x = 1 for 0° ≤ x < 360°.
- sin x =
- Reference angle is 30°.
- Sine is positive in quadrants I and II.
Answer: x = 30°, 150°
Higher Mathematics
Higher Maths Solving trigonometric equations
Practise solving trigonometric equations for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Solve trigonometric equations in degrees or radians over a stated interval.
Before you start
- Know exact values for 0°, 30°, 45°, 60° and 90°.
- Understand CAST or graph symmetry.
- Check the interval stated in the question.
Explanation
Trig equations usually have more than one solution in a given interval. Find the related acute angle, then use symmetry or graphs to list all valid solutions.
Always finish by checking the interval and the original equation.
Visual support
Amplitude is the vertical distance from the midline; period is the horizontal length of one cycle
Method and rules
- sin x positive in quadrants I and II.
- cos x positive in quadrants I and IV.
- tan x positive in quadrants I and III.
- sin² x + cos² x = 1
Worked examples
Worked example 2
Solve a cosine equation
Solve cos x = − for 0° ≤ x < 360°.
- Reference angle is 60°.
- Cosine is negative in quadrants II and III.
So: x = 120°, 240°
Worked example 3
Solve a tan equation
Solve tan x = 1 for 0° ≤ x < 360°.
- Reference angle is 45°.
- Tangent is positive in quadrants I and III.
Answer: x = 45°, 225°
Watch out
- Giving only the calculator's first answer.
- Including endpoints that are not in the interval.
- Losing solutions after squaring or rearranging.
Exam reminder
List every solution in the stated interval and check whether endpoints are included. Keep exact values when exact angles are expected.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.