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

(write these down on an index card) Trigonometric Identities (write these down on an index card) Quotient Identities: Reciprocal Identities: Pythagorean Identities: sin2q + cos2q = 1 tan2q + 1 = sec2q cot2q + 1 = csc2q Sin2q = 1 - cos2q tan2q = sec2q - 1 cot2q = csc2q - 1 cos2q = 1 - sin2q

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

Do you remember the Unit Circle? Where did our Pythagorean Identities come from? Do you remember the Unit Circle? What is the equation for the unit circle? x2 + y2 = 1 What does x = ? What does y = ? (in terms of trig functions) Sin2 θ + cos2 θ = 1 Pythagorean Identity!

Take the Pythagorean Identity and discover a new one! Hint: Try dividing everything by cos2θ sin2θ + cos2θ = 1 . cos2θ cos2θ cos2θ tan2θ + 1 = sec2θ Quotient Identity Reciprocal Identity another Pythagorean Identity

Take the Pythagorean Identity and discover a new one! Hint: Try dividing everything by sin2θ sin2θ + cos2θ = 1 . sin2θ sin2θ sin2θ 1 + cot2θ = csc2θ Quotient Identity Reciprocal Identity a third Pythagorean 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