Trigonometric Identities PDF

TRIGONOMETRIC IDENTITIES Identity Equation Verifying an Identity: Verify:.  An identity is an equation that is true for all values of the variable in the domain of the equation. An equation that is not an identity is called a conditional equation. In other words, if some values of the variabl...

TRIGONOMETRIC IDENTITIES Identity Equation Verifying an Identity: Verify:.  An identity is an equation that is true for all values of the variable in the domain of the equation. An equation that is not an identity is called a conditional equation. In other words, if some values of the variable in the domain of the equation do not satisfy the equation, then the equation is conditional.  FUNDAMENTAL TRIGONOMETRIC IDENTITIES Reciprocal Identities  Quotient Identities tan x = cot x = Pythagorean Identities Even-Odd Identities  Guidelines for Verifying Trigonometric Identities 1. Work with each side of the equation independently of the other side. Start with the more complicated side and transform it in a step- by-step fashion until it looks exactly like the other side. 2. Analyze the identity and look for opportunities to apply the fundamental identities. 3. Try using one or more of the following techniques: Rewrite the more complicated side in terms of sines and cosines. Factor out the greatest common factor.  Separate a single-term quotient into two terms: and Combine fractional expressions using the least common denominator. Multiply the numerator and the denominator by a binomial factor that appears on the other side of the identity.  Note: Do not be afraid to stop and start over again if you are not getting anywhere. Creative puzzle solvers know that strategies leading to dead ends often provide good problem- solving ideas. Example: Verify the identity: csc θ – cot θ = Example: Verify the identity: Example: Verify the identity: cos x – cos x sin 2 x= cos 3 x Example: Verify the identity: = sec x + tan x Below are other Trigonometric Identities: Sum and Difference Double Angle Half Angle Seatwork: Prove the following identities.