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Elementary Calculus Trigonometric Functions Trigonometry Trigonometric Identities
 

Trigonometric Identities

Here is a table of trigonometric identities. The diagrams in Figure 7.1.12 suggest possible proofs. ((6) and (7) are called the addition formulas.)

(1)

sin2 θ + cos2 θ = 1

07_trigonometric_functions-31.gif

(Figure 7.1.12(a))

(2)

tan2 θ + 1 = sec2 θ

07_trigonometric_functions-32.gif

(Figure 7.1.12(b))

(3)

cot2 θ + 1 = csc2 θ

07_trigonometric_functions-33.gif

(Figure 7.1.12(c))

(4)

sin (-θ) = -sin θ, cos(-θ) = cosθ

(Figure 7.1.12(d))

(5)

sin (π/2 - θ) = cos θ, cos (π/2 - θ) = sin θ

07_trigonometric_functions-34.gif

(Figure 7.1.12(e))

(6)

sin (θ + φ) = sin θ cos φ + cos θ sin φ

07_trigonometric_functions-35.gif

(Figure 7.1.12(f))

(7)

cos (θ + φ) = cos θ cos φ - sin θ sin φ

07_trigonometric_functions-36.gif

(Figure 7.1.12(f))

Last Update: 2006-Nov-05