Trig Identities Packet

Transcription

1 Advanced Math Name Trig Identities Packet = = = = = = = = cos 2 θ + sin 2 θ = sin 2 θ = cos 2 θ cos 2 θ = sin 2 θ + tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ + cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ March 206 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 3 4 Review 5 Quiz Trig Identities [D] HW: Packet Pg. 5 #-8 [Ans. Key Pg. 2] 7 Trig Identities [D2] HW: Packet Pg. 8-9 #-2 [Ans. Key Pg. 2] 8 Trig Identities [D3] HW: Packet Pg. #-8 [Ans. Key Pg. 2] 20 2 Review Trig Identities: Odds 22 Review Trig Identities: Evens 23 Quiz Trig Identities No Classes- Spring Break 26

2 Advanced Math Trigonometric Identities [Day ] NOTES = = = = Pythagorean Identity Solve the Pythagorean Identity for cos 2 θ Solve the Pythagorean Identity for sin 2 θ Take the Pythagorean Identity and divide every single term by cos 2 θ cos 2 θ + sin 2 θ = Solve the above equation for tan 2 θ Take the Pythagorean Identity and divide every single term by sin 2 θ cos 2 θ + sin 2 θ = Solve the above equation for cot 2 θ Some other identities: = = = 2

3 = = = = = = = = cos 2 θ + sin 2 θ = sin 2 θ = cos 2 θ cos 2 θ = sin 2 θ + tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ + cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ Example : Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. a. b. cos2 θ cos 2 θ c. d. Example 2: Simplify the complex fraction. a b c d

4 = = = = = = = = cos 2 θ + sin 2 θ = sin 2 θ = cos 2 θ cos 2 θ = sin 2 θ + tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ tan 2 θ = sec 2 θ + cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ cot 2 θ = csc 2 θ Example 3: Simplify the complex fraction. a. b. cos2 θ tan 2 θ c. d. 4

5 Advanced Math Trigonometric Identities [Day ] HOMEWORK Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant.. 2. sin2 θ sin 2 θ.) 2.) ) 4.) Simplify the complex fraction sin2 θ cot 2 θ 5.) 6.) ) 8.) 5

6 Advanced Math Trigonometric Identities [Day 2] NOTES Example : Simplify a. + b. cos2 θ c. sec2 θ sec 2 θ d. To VERIFY AN IDENTITY: Work on each side separately and make sure you don t move things from one side to the other! You can work on both sides at the same time but you just can t move things from one side to the other. Verify the identity. Example : = Example 2: 2sin 2 θ = 2cos 2 θ Example 3: Factor a. a 2 a 2 b b. x 2 2x + 6

7 Example 4: Verify the identity. csc 2 θ cos 2 θcsc 2 θ = Example 5: Simplify a. ( )( + ) There are two different ways you can leave this answer! In the notes, leave it in terms of sin 2 θ. In the homework, you will be verifying and leaving it in terms of cos 2 θ b. ( + ) 2 c. sin 2 θ 2 + 7

8 Advanced Math Trigonometric Identities [Day 2] HOMEWORK Simplify the complex fraction.. 2. sin 2 θ +.) 2.) 3. csc2 θ csc 2 θ 4. 3.) 4.) Verify the identity. Both sides should end up being equal, so you will not find these on the answer key. 5. = 6. ( )( + ) = 2cos 2 θ 7. + = 8. sin 2 θ( + cot 2 θ) = 8

9 Verify the identity. Both sides should end up being equal, so you will not find these on the answer key. 9. = sin 2 θ 0. =. + tan2 θ = 2. ( )( + ) = csc 2 θ 9

10 Advanced Math Trigonometric Identities [Day 3] NOTES Example : Simplify a b. + c. + + d. sec2 θ e. + f. + 0

11 Advanced Math Trigonometric Identities [Day 3] HOMEWORK Simplify csc 2 θ Verify the identity. Both sides should end up being equal, so you will not find these on the answer key sec 2 θ sec 2 θ = + cos2 θ 4. + = 5. sec 2 θ sin 2 θsec 2 θ = 6. sin 2 θ 2 + = csc2 θ

12 SOLUTIONS D. 2. cot 2 θ sin 2 θ cos 2 θ D2. cos 2 θ cos 2 θ 4. tan 2 θ D