Quick answer: For angles 0°, 30°, 45°, 60°, 90°, sine values are 0, 1/2, 1/√2, √3/2, 1. Cosine values reverse that list: 1, √3/2, 1/√2, 1/2, 0. Tangent equals sine divided by cosine.
Worked example
Evaluate 2 sin30° + cos60° − tan45°.
- Use sin30° = 1/2, cos60° = 1/2 and tan45° = 1.
- Then 2(1/2) + 1/2 − 1 = 1/2.
- Tangent values at 0°, 30°, 45°, 60° are 0, 1/√3, 1, √3; tan90° is undefined.
Check the result
The result is 1 + 0.5 − 1 = 0.5.
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Common mistake to avoid
tan90° is not a real number and should not be written as zero. Ensure a calculator is in degrees for this table.
Try it yourself
1. Evaluate sin²45° + cos²45°. 2. Evaluate sin60°/cos30°.
Answers and reasoning
1. 1/2 + 1/2 = 1. 2. (√3/2)/(√3/2) = 1.
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