Choose the reference angle and identify the right sides before using sine, cosine, or tangent. Connect each ratio to similar right triangles.
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Trigonometry
Connect right-triangle side ratios to angles and the unit circle. Identify the reference angle, use sine and cosine, and distinguish degrees from radians.
Find the topic you need
Explore trigonometry
Connect an angle to a point on the unit circle. Read sine and cosine as coordinates, identify their signs, and relate degrees to radians.
What you’ll learn
- Identify opposite, adjacent, and hypotenuse relative to an angle.
- Use a trigonometric ratio to relate an angle and side lengths.
- Connect sine and cosine to coordinates on the unit circle.
Triangle ratios depend on the chosen angle
Similar right triangles with the same acute angle have the same corresponding side ratios. Sine, cosine, and tangent name those relationships. The opposite and adjacent sides change when you choose the other acute angle.
The unit circle extends the idea
A circle of radius one connects an angle to a point with coordinates (cos θ, sin θ). This gives meaning to angles beyond a right triangle and helps explain signs in different quadrants.
Keep angle units explicit
Degrees and radians measure the same angle using different units. Check the problem and calculator mode before interpreting a value, especially when moving toward calculus.
Keep exploring
Right-triangle ratiosChoose the reference angle and identify the right sides before using sine, cosine, or tangent. Connect each ratio to similar right triangles.The unit circleConnect an angle to a point on the unit circle. Read sine and cosine as coordinates, identify their signs, and relate degrees to radians.Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.
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