Precalculus, Unit 5: Trigonometric Identities and Equations. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is the Pythagorean identity for sine and cosine?
- sin^2(x) + cos^2(x) = 1
- What is the Pythagorean identity involving tangent and secant?
- 1 + tan^2(x) = sec^2(x)
- What is the Pythagorean identity involving cotangent and cosecant?
- 1 + cot^2(x) = csc^2(x)
- What is a reciprocal identity for cosecant?
- csc(x) = 1/sin(x)
- What is a reciprocal identity for secant?
- sec(x) = 1/cos(x)
- What is a quotient identity for tangent?
- tan(x) = sin(x)/cos(x)
- What is the sine sum formula?
- sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
- What is the cosine sum formula?
- cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
- What is the sine difference formula?
- sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
- What is the cosine difference formula?
- cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
- What is the double angle formula for sine?
- sin(2x) = 2 sin(x) cos(x)
- What is one form of the double angle formula for cosine?
- cos(2x) = cos^2(x) - sin^2(x)
- What is a half-angle formula used for?
- Finding trigonometric values of half an angle from the original angle's value
- What does it mean to 'verify' a trigonometric identity?
- Show that both sides of the equation are equal for all valid values
- What is a common strategy for verifying trigonometric identities?
- Rewrite both sides in terms of sine and cosine, then simplify
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