Explanation
Trigonometric functions relate angles to ratios of side lengths in a right triangle, or equivalently, to coordinates on the unit circle.
The three primary trigonometric functions are:
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sin(θ) = opposite / hypotenuse
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cos(θ) = adjacent / hypotenuse
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tan(θ) = opposite / adjacent
In precalculus, you are expected to know exact trig values for certain angles without a calculator.
These angles are:
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0°, 30°, 45°, 60°, 90°
All of these angles lie in the first quadrant, where:
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sin(θ) > 0
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cos(θ) > 0
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tan(θ) > 0
Exact values:
| Angle | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
These values come from special right triangles and the unit circle.
Quiz (5 Questions)
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What is sin(60°)?
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What is cos(30°)?
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What is tan(45°)?
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Why is tan(90°) undefined?
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Are sine and cosine positive in the first quadrant?
Answer Key
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√3/2
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√3/2
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1
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Division by zero
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Yes