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Precalculus / Trigonometry
Trigonometric Identities
12 terms · by ineedtostudy · updated 4 hours ago
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Terms in this set
Pythagorean identity
sin²θ + cos²θ = 1
Pythagorean, tangent form
1 + tan²θ = sec²θ
Pythagorean, cotangent form
1 + cot²θ = csc²θ
sin(A ± B)
sin A cos B ± cos A sin B
cos(A ± B)
cos A cos B ∓ sin A sin B — note the sign flips.
Double angle, sine
sin 2θ = 2 sin θ cos θ
Double angle, cosine
cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ
Law of sines
a/sin A = b/sin B = c/sin C
Law of cosines
c² = a² + b² − 2ab cos C. Reduces to Pythagoras when C is 90°.
Even and odd
cos(−θ) = cos θ (even); sin(−θ) = −sin θ (odd).
Radians to degrees
Multiply by 180/π. π radians is 180°.
Unit circle at 30-45-60
sin: 1/2, √2/2, √3/2. cos is the same list reversed.