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Definition
Trigonometric ratios are relationships between the angles and side lengths of a right triangle. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). For a given acute angle in a right triangle:
- Sine (sin) is the ratio of the length of the opposite side to the hypotenuse.
- Cosine (cos) is the ratio of the length of the adjacent side to the hypotenuse.
- Tangent (tan) is the ratio of the length of the opposite side to the adjacent side.
These ratios can also be extended beyond right triangles using the unit circle.
Summary
Trigonometric ratios help describe the relationship between angles and sides in right triangles. They are essential for solving problems involving angles, distances, and heights in geometry, physics, engineering, and other fields. By using sine, cosine, and tangent, you can find missing side lengths or angle measures. Trigonometric ratios also connect to the unit circle, allowing them to be used for angles of any measure, not just those in right triangles.
Trigonometric Ratios Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Trigonometric Ratios. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- SOH–CAH–TOA Sort & Solve
- Missing Side Using a Trig Ratio
- “Find the Angle” (Inverse Trig)
- Angle of Elevation
- Exact Trig Values
- Pythagorean Theorem + Trig Ratios Combo
- Which Ratio Fits?
- Solve the Entire Triangle
- Tangent Application
- Correct the Error