The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Home Trigonometric Functions Trigonometry Trigonometric Identities
 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

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))

Home Trigonometric Functions Trigonometry Trigonometric Identities

Last Update: 2006-11-05