All over China, parents tell their children to stop complaining and to finish their quadratic equations and trigonometric functions because there are sixty-five million American kids going to bed with no math at all.

Michael Cunningham

sections:

      5.1, 5.2, 5.3, and 5.5

Trigonometric identities permit you to evaluate complicated combinations of trig functions in terms of simpler expressions. The key in verifying identities is not to move any value from one side of the equation to the other; that is, manipulate one side so that it matches the original other side. This ensures that you do not introduce extraneous results as we did in squaring both sides of an equation to remove a radical.

objectives:

• derive other identities based upon the pythagorean identity
• give the parity and symmetry of the trigonometric functions
• apply the trigonometric identities to simplify expressions involving these functions
• express the trigonometric identities
• use the trigonometric identities to evaluate a trigonometric function
• use the pythagorean relation and identities to derive other identities
• prove a trigonometric identity
• simplify a trigonometric expression
• write out the addition and subtraction identities
• use the cofunction identities
• derive simple trigonometric identities
• derive the double-angle identities from the addition identities
• use the half-angle identities
• prove identities involving double-angle and half-angle identities
• solve trignometric equations