Year 9 - Maths
The unit circle
Trigonometry
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.
Lesson Summary
You will learn to appreciate that the trigonometric functions are derived from measurements within a unit circle.
Key Notes
- The unit circle is a circle with a radius of one.
- The unit circle is centered on the origin.
- The sine of an angle is the y-coordinate of the point where the radius has been rotated through that angle.
- The cosine of an angle is the x-coordinate of the point where the radius has been rotated through that angle.
- The tangent of an angle is the length of the side opposite the angle along the tangent at x = 1 to the unit circle.
Vocabulary To Learn
- Trigonometric functions: Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
- Sine function: The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
- Cosine function: The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
- Tangent function: The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common Mistakes To Avoid
- When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The unit circle is a circle with a radius of one. The unit circle is centered on the origin.
2. Use this key word in a maths sentence and explain it clearly. 'Trigonometric functions'
Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate. Correction: Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. However, two decimal places is a reasonable degree of accuracy for reading values from the graphs during this lesson.
More Lessons In This Unit
- Checking and securing understanding of Pythagoras' theorem Study Guide
- Checking and securing understanding of similar triangles Study Guide
- Choosing an appropriate method for finding lengths of a triangle Study Guide
- Choosing the right trigonometric ratio Study Guide
- Problem solving with trigonometry Study Guide
- Scaling the right-angled triangle from the unit circle Study Guide
- Sine and cosine ratios Study Guide
- Tangent ratio Study Guide
- Using the cosine ratio Study Guide
- Using the sine ratio Study Guide
- Using the tangent ratio Study Guide
Browse all guides in the Year 9 Maths guide library.