Special Angle Values
Exact values for 30°, 45°, 60°.
Key idea
Exact values for 30°, 45°, 60°.
In depth
For 0°, 30°, 45°, 60°, 90° the values are exact. sin: 0, 1/2, √2/2, √3/2, 1. cos is the reverse. tan: 0, √3/3, 1, √3, undefined. They come from the 45-45-90 and 30-60-90 triangles.
Worked example
sin 30° = 1/2; cos 60° = 1/2; tan 45° = 1; sin 60° = √3/2.
Formula
Real-world uses
- Exact calculations for 45° roof slopes and 30°–60° triangles without a calculator
Common mistake
Swapping 30° and 60° values.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Special Angle Values?
Exact values for 30°, 45°, 60°. It is a topic at the intermediate level in Trigonometry.
What is the formula for Special Angle Values?
The key formula is sin30° = 1/2, cos45° = √2/2, tan60° = √3.
Where is Special Angle Values used in real life?
Real-world examples: Exact calculations for 45° roof slopes and 30°–60° triangles without a calculator.
What should I learn before Special Angle Values?
Make sure you are comfortable with Angles of Elevation and Depression, the previous topic in Trigonometry.
What is a common mistake with Special Angle Values?
Swapping 30° and 60° values.
How can I practise Special Angle Values?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Special Angle Values?
Move on to Unit Circle next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.