CC3: Prove and Apply Trigonometry Identities LT: 1F I can prove the Pythagorean identity sin2θ+cos2θ=1 and use it to find sinθ, cosθ, or tanθ given sinθ, cosθ, or tanθ and the quadrant.

A.) The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trig. Functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions, from which all others may be derived. I.) Prove and Apply Trigonometric Identities

A. Definition Pythagorean Trigonometric Identity sin 2 (x) + cos 2 (x)= 1 Pythagorean Trigonometric Identity sin 2 (x) + cos 2 (x)= 1 Sum and Difference Formulas sin(A±B)=sin(A)cos(B)±cos(A)sin(B) cos(A±B)=cos(A)cos(B) sin(A)sin(B) Sum and Difference Formulas sin(A±B)=sin(A)cos(B)±cos(A)sin(B) cos(A±B)=cos(A)cos(B) sin(A)sin(B) Notice the plus/min us Notice the order

B. Visual Using what we know about the Pythagorean Theorem we can write x 2 + y 2 = 1 2 To show the relation ship between the side lengths of the right triangle x 2 + y 2 = 1 Using what we know about the Unit Circle we can replace x and y with. cos 2 x + sin 2 x = 1

Goal Problems (LT 1E) Recall & Reproductions Suppose that cosθ=2/5 and that θ is in the 4th quadrant. Find sinθ and tanθ exactly. Routine Given x is in Quadrant I, find the value of x that makes this statement true.

Goal Problems Answers (LT 1E) Recall & Reproductions Routine Is Sine neg. or pos. in Q4?

Active Sense-Making Recall & Reproductions Sideways Sheet Down at desk Routine Round Robin around the room Based on your Goal Problems make your plan of attack for today’s practice