{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ch.9 Trigonometric Identities and Their Applications

# ch.9 Trigonometric Identities and Their Applications -...

This preview shows pages 1–9. Sign up to view the full content.

Chapter 9 Trigonometric Identities and Their Applications 9.1 Identities, Expressions and Equations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Key Points The difference between an equation and an identity The Pythagorean and double angle identities
Identities (8, 16) Pythagorean Quotient 2 2 2 2 2 2 sin cos 1, tan 1 sec , 1 cot csc θ + = + = + = sin tan cos cos cot sin = =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Double-Angle Identities 2 2 2 2 2 cos2 cos sin cos2 1 2sin cos2 2cos 1 sin 2 2sin cos 2tan tan 2 1 tan A A A A A A A A A A A A A = - = - = - = = -
Using Identities to Solve Equations Example 7 Find all solutions to the equation sin 2 t = 2 sin t on the interval 0 ≤ t ≤ 2π. Functions Modeling Change: A Preparation for Calculus, 4th

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Using Identities to Solve Equations Functions Modeling Change: A Preparation for Calculus, 4th y = sin 2 t y = 2 sin t
Hints for Verifying Identities 1. Learn the fundamental identities given in the last section. Whenever you see either side of a fundamental identity, the other side should come to mind. Also, be aware of equivalent forms of the fundamental identities. For example is an alternative form of the identity 2. Try to rewrite the more complicated side of the equation so that it is identical to the simpler side. 2 2 sin 1 cos θ = - 2 2 sin cos 1. + =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hints for Verifying Identities continued 3. It is sometimes helpful to express all trigonometric functions in the equation in terms of sine and cosine and then simplify the result. 4.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 34

ch.9 Trigonometric Identities and Their Applications -...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online