Chapter 5 Trigonometric Identities Objective SWBAT use the

Chapter 5 Trigonometric Identities Objective: SWBAT use the fundamental identities of Trigonometry functions to find trigonometric functions values given one value and the quadrant.

Trigonometric Identities (write these down on an index card) Quotient Identities: Reciprocal Identities: Pythagorean Identities: sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 cot 2 + 1 = csc 2 Sin 2 = 1 - cos 2 tan 2 = sec 2 - 1 cot 2 = csc 2 - 1 cos 2 = 1 - sin 2

Trigonometric Identities (write these down on an index card) Negative-Angle Identities:

Where did our Pythagorean Identities come from? Do you remember the Unit Circle? What is the equation for the unit circle? x 2 + y 2 = 1 What does x = ? What does y = ? (in terms of trig functions) Sin 2 θ + cos 2 θ = 1 Pythagorean Identity!

Take the Pythagorean Identity and discover a new one! Hint: Try dividing everything by cos 2θ sin 2θ + cos 2θ = 1. cos 2θ tan 2θ + 1 = sec 2θ Quotient Identity another Pythagorean Identity Reciprocal Identity

Take the Pythagorean Identity and discover a new one! Hint: Try dividing everything by sin 2θ + cos 2θ = 1. sin 2θ 1 + cot 2θ = csc 2θ Quotient Identity a third Pythagorean Identity Reciprocal Identity

Using the identities you now know, find the trig value : If and is in quadrant II, find sec . Look for an identity that relates tangent and secant.

Using the identities you now know, find the trig value : If and is in quadrant II, find cot ( )

Using the identities you now know, find the trig value. 1. ) If cosθ = 3/5, find csc θ.

Using the identities you now know, find the trig value. 2. ) If cosθ = 3/4, find secθ