Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Sine and cosine of complementary angles
Explain and use sine cosine relationships for complementary angles
Problem types
- Sine and cosine of complementary angles
- Sine equals cosine of acute angles
Builds on
- Sine, cosine, and tangent
- Theorems about similar triangles · Earlier idea
The altitude to the hypotenuse makes two right triangles similar to the original, which shows the sine of one acute angle is the cosine of the other.
Leads to
- Modeling with geometry · See it applied
Complementary angle relations let one trig ratio find a height or distance in a modeling problem.
- Pythagorean and angle-sum identities · Extend the idea
Cofunction relations are identities that hold for every angle and are used to rewrite expressions.
- Odd, even, and periodic trig functions · Extend the idea
The cofunction relation sin(90 - x) = cos x is one of the symmetries of the sine and cosine on the unit circle.
Related skills
- The laws of sines and cosines · Shared foundations
- Side ratios of special right triangles · Shared foundations
- Area from two sides and the included angle · Shared foundations
- Vectors and their components · Shared foundations
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