Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Pythagorean and angle-sum identities
Establish and use Pythagorean and angle-sum identities
Problem types
- Identities and angle sums
- Find the cosine of an angle from its tangent and quadrant
Builds on
- Radians and the unit circle
- Writing and critiquing a geometric proof
- Exact values at special angles · Useful idea
Angle-sum formulas combine the exact values at 30°, 45° and 60° to give exact values at angles such as 15° and 75°.
- Sine and cosine of complementary angles · Earlier idea
Cofunction relations are identities that hold for every angle and are used to rewrite expressions.
- Why each equation step is valid · Useful idea
Proving a trigonometric identity is a chain of equal expressions, each step justified by a property.
Leads to
- Solving trigonometric equations
- The complex plane · See it applied
The identity cos squared + sin squared = 1 shows the complex number cos t + i sin t has modulus 1.
- Motion described by a parameter · See it applied
The identity cos squared + sin squared = 1 turns x = cos t, y = sin t into the equation of a circle.
Related skills
- Proving a polynomial identity · Related idea
Algebraic identities such as the difference of squares are used to prove trigonometric identities.
- Theorems about circles · Shared foundations
- Congruence criteria for triangles · Shared foundations
- Proofs that use coordinates · Shared foundations
- Proofs about lines and angles · Shared foundations
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