Algebra2/Trig Chapter 12 Packet

Transcription

1 Algebra/Trig Chapter 1 Packet In this unit, students will be able t: Learn and apply the sum and difference identities Learn and apply the duble-angle identities Learn and apply the ½-angle identities Name: Teacher: Pd: 1

2 Table f Cntents Day 1: Sum and Difference f Angles Identities SWBAT: Find trignmetric functin values using sum, and difference frmulas Pgs. 4 8 in Packet HW: Pgs in Packet Day : Duble Angle Identities SWBAT: Find trignmetric functin values using sum, difference, duble, and half angle frmulas Pgs in Packet HW: Pgs in Packet Day 3: Half Angle Identities SWBAT: Find trignmetric functin values using sum, difference, duble, and half angle frmulas Pgs. 19 in Packet HW: Pgs. 3 4 in Packet Day 4: Review SWBAT: Find trignmetric functin values using sum, difference, duble, and half angle frmulas Pgs. 5 7 in Packet HW: Pgs. 5 7 in Packet Day 5: Test

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4 Day 1: Sum and Difference Frmulas fr Sine and Csine SWBAT: find trignmetric functin values using sum, and difference frmulas Recall that lgarithms dn t distribute the way peple wuld THINK they wuld: (d yu remember what it is?) Sines and csines dn t distribute like yu think, either. With yur calculatr, prve that ( ) when A=30 and B=45. Cncept 1: Sum and Difference f Angles 4

5 Example 3: Find tan (A + B) if tan A = 3 and tan B = 1 ) 3) 4) 5

6 Example : Find the exact value f 6

7 Example 3: Example 4: 7

8 Summary/Clsure: Exit Ticket ) 8

9 Day 1 - Hmewrk 1. Find the exact functin value f cs135 by using cs(90 45 ).. Find the exact functin value f cs195 by using cs( ). 3. If 1 cs( A 30 ), then the measure f A may be (1) () (3) 30 () (4) Find tan (A B) if tan A = 4 3 and tan B = The value f (cs67 )(cs3 ) (sin67 )(sin 3 ) is (1) 1 () (3) (4) 0 6. Find the exact value f sin 75 by evaluating sin(45 30 ) If B is acute and sin B, find the value f sin( 90 B) If sin x = and cs y =, and x and y are psitive acute angles, find tan (x + y)

10 9. The expressin tan ( 180 y ) is equivalent t (1) tan y () tan y (3) 0 (4) If sin x,cs y, and x and y are the measures f angles in the first quadrant, 5 5 find the value f sin( x y). 11. The expressinsin 40 cs15 cs40 sin15 is equivalent t (1) sin 55 () sin 5 (3) cs 55 (4) cs If sin A, A is in Quadrant I, csb,and B is in Quadrant II, find cs( A B) If sin x, x is the measure f an angle in Quadrant III, cs y, and y is the measure f an angle 13 5 in Quadrant II, find cs( x y). 14. Find the exact value f cs105 by using cs( ). 10

11 1 15. If sin A, A is in Quadrant III, 13 cs( A B). 4 sin B, and B is in Quadrant II, find The expressin cs30 cs1 sin 30 sin1 is equivalent t (1) () (3) cs 4 () cs4 sin 4 (4) cs 18 cs 4 sin The expressin sin( x) is equivalent t 6 (1) 1 3 sin x () sin x (3) cs x sin x (4) cs x sin x 18. If sin( A 30 ) cs60, the number f degrees in the measure f A is (1) 30 () 60 (3) 90 (4) If x and y are the measures f psitive acute angles, sin x, andsin y, then sin( x y) equals (1) 10 3 () (3) (4) Find tan (A + B) if angle A is in the secnd quadrant, sin A = 0.6, and tan B = 4. 11

12 Day : Duble Angle Identities SWBAT: find trignmetric functin values using duble angle frmulas Warm - Up What are the sine, csine, and tangent ratis? If = and, what is the value f? Name 3 sets f Pythagrean s triples? 1),, ),, 3),, Lessn: What is a duble-angle functin? Where can yu find the duble-angle Identities? 1

13 Cncept 1: Sine Duble-Angle Identity Mdel Prblem Step 1: Create a right triangle Student Prblem If is an acute angle such that, what is the value f sin? Step : Find the rati fr = Step 3: plug int duble-angle Frmula Mdel Prblem 1 If cs A and A is in Quadrant III, express, in 3 fractinal frm fr sin? Student Prblem 4 If cs A and A is in Quadrant II, express, in 7 fractinal frm fr sin? Step 1: Create a right triangle Step : Find the rati fr = Step 3: plug int duble-angle Frmula 13

14 Cncept : Csine Duble-Angle Identity Mdel Prblem If is an acute angle such that, what is the value f cs? Step 1: Decide which csine duble angle frmula t use Student Prblem If is an acute angle such that, what is the value f cs? Step 1: Decide which csine duble angle frmula t use Step : plug int crrect duble-angle Frmula Step : plug int crrect duble-angle Frmula Cncept 3: Tangent Duble-Angle Identity Mdel Prblem 4 If cs A and A is in Quadrant I, find the psitive 5 value f tan. Step 1: Create a right triangle Student Prblem 1 If sin A, where 70 find the 13 value f tan. Step 1: Create a right triangle Step : Find the rati fr = Step 3: plug int duble-angle Frmula Step : Find the rati fr = Step 3: plug int duble-angle Frmula 14

15 SUMMARY Exit Ticket 15

16 Day - Hmewrk 1.Write the identity fr sin x =. Write the identity fr the csx in terms f: a. sin x and cs x b. csx nly c. sin x nly 3. Write the identity fr tan x = 4 4. If cs A and A is in Quadrant III, express, in fractinal frm, each value: 5 a. sin A b. cs A c. sin A d. tan A 16

17 3 5. If sin A and A is in Quadrant III, find: 5 a. sin A b. cs A c. tan A d. The quadrant in which Aterminates 1 6. If cs A and A is acute, find 3 a. sin A b. cs A c. tan A 7. If cs sin, then cs is equivalent t (1) 1 () 0 (3) cs (4) sin 17

18 8. The expressin (sin x csx) is equivalent t (1) 1 () sin x cs x (3) 1 csx (4) 1 sin x 9. If sin is negative and sin is psitive, then cs (1) Must be psitive (3) Must be 0 () Must be negative (4) May be psitive r negative If tan and is a secnd quadrant angle, find: 3 a. sin b. cs c. tan 11. If sec = 13 and is in the furth quadrant, find tan. 1. If = 5, find tan. 18

19 Day 3: Half Angle Identities SWBAT: find trignmetric functin values using half angle frmulas Warm - Up What are the sine, csine, and tangent ratis? If is lcated in Quadrant II, such that =, what is the value f? If is an acute angle, such that =, what is the value f? If =, what is the negative value f? Lessn: What is a half-angle functin? Where can yu find the half-angle Identities? 19

20 Mdel Prblem Student Prblem If, what is the negative value f sin? Step 1: plug int half-angle Frmula If, what is the negative value If, what is the psitive value f f tan? tan? 0

21 Mdel Prblem 4 If tan A and A is in Quadrant III, find the 7 psitive value f sin. Step 1: Create a right triangle Student Prblem sin. If A 6 and A is in Quadrant I, find the negative value f cs. Step 1: Cnvert.6 t a fractin. Step : Create a right triangle Step : Find the rati fr = Step 3: plug int half-angle Frmula Step 3: Find the rati fr = Step 4: plug int half-angle Frmula 1

22 SUMMARY Exit Ticket

23 Day 3 Hmewrk 3

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25 Day 4 Review f Trig Cncepts 5

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28 If x is the measure f a psitive acute angle and csx, find the value f sin x The expressin 1 cs80 is equivalent t (1) 1 sin 80 () sin 40 (3) 1 cs40 (4) cs If 180 A 70 and sin A = 5 1, find tan A. 3 8