Mon., Nov. 5 Test Over Sine And Cosine And And Cotangent . - Precalculus

Mon., Nov. 5th Test over Sine and Cosine and Applications Tue., Nov 6th Graphing Secant, Cosecant, Tangent and Cotangent Functions Book reference Sec 4.6 p. 332 Assignment Day 1 Graphing Wed., Nov 7th Graphing Others Day 2 Graphing plus Asymptote worksheet Thurs., Nov 8th Writing Equations and Graphing Writing Worksheet # 1 & 2 Fri., Nov 9th QUIZ over Other Graphing Begin Graphing Inverse Trig Functions Assignment Graphing Inverse Mon., Nov 12th Inverse Angles and Values Day 1 Packet plus text p. 350 # 59-64 Tue., Nov 13th Inverse Values and Angles Day 2 Worksheet Wed., Nov 14th QUIZ Thurs., Nov 15th Review Game Study for Test Fri., Nov 16th Test over 4.3,4.6,4.7 No Homework Sec 4.3 in text Assignment Packet p. 17 plus review 1

GRAPHING ALL SIX TRIG FUNCTIONS y cos Basic shape Domain Range y sec Basic shape Domain Range Equation of asymptotes Two specific asymptotes y tan Basic shape Domain Range Equation of asymptotes Two specific asymptotes 2

y sin Basic shape Domain Range y csc Basic shape Domain Range Equation of asymptotes Two specific asymptotes y cot Basic shape Domain Range Equation of asymptotes Two specific asymptotes 3

Day 1 1) GRAPHING y tan x 2 Domain Range Equation of asymptotes Two specific asymptotes 2) y cot 4 Domain Range Equation of asymptotes Two specific asymptotes 3) y 2sec Domain Range Equation of asymptotes Two specific asymptotes 4) y 1 csc x 2 1 Domain Range Equation of asymptotes Two specific asymptotes 4

5) y 3sec x 1 6 Domain Range Equation of asymptotes Two specific asymptotes 6) y csc 3 2 3 Domain Range Equation of asymptotes Two specific asymptotes 7) y 2 tan 2x 3 Domain Range Equation of asymptotes Two specific asymptotes 8) y cot 1 2 2 Domain Range Equation of asymptotes Two specific asymptotes 5

PRECALCULUS TRIG EQUATIONS AND THEIR ASYMPTOTES Match the equation with its asymptotes. Equation Asymptotes 1. y ½tan x 3 A. 2. y 2sec x B. 3. y csc 2x - 4 C. 4. y tan x 2 D. k 2 5. y sec ½x 4 E. π 2k 6. y -3cotx – 2 F. 2kπ 7. y cot (x - 8. y sec ½ x 9. y csc (2x - 10. y tan (x 11. y sec (x - 12. y tan (2x 13. y -4 tan ½x 3 14. y csc ½x 3 15. y cot(x - 16. ) 2 2 G. kπ 2 k 4 4 k 2 k ) ) 2 ) 2 2 ) ) 4 y 5sec(2x ) 1 6

Graphing Trig Functions Day 1 Find the period, domain and range of each function. Find the general equation of the asymptotes and two specific asymptotes on all sec ,csc , tan , and cot functions. 1) y tan x 2) y 4) y csc x 5) y 3sec x 7) y 2 tan 2x 3 8) y cot 10) y 2csc 2x 1 11) y 3cot x 2 1 cot 4 1 6 1 2 2 6 1 3) y sec 6) y 9) y 12) y csc 3 3 2 1 sec 2 x 2 2 3 tan x 2 6 1 Day 2 Graphing Others Day 2 Graph one cycle of each function. 1 4 1. y tan x y 2. 3sec x 3. 2 y csc 3 x 1 4 Graph and state whether each function is odd, even or neither. y tan x 4. 5. 2 y cot(x) 2 If F is any function with period 5, determine the period of each related function. Provide a reason for your answer. 6. y F(x 1) 7. y F(x) 5 y 8. F 1 x 2 9. y F(3x) Graph one cycle of each function. 10. y tan 2x 4 3 1 11. y 3csc 2x 4 3 1 GRAPHING INVERSE TRIG FUNCTIONS Find the domain, range, and sketch a complete graph of each function. Inverse functions are denoted by y sin 1 x or by y A rcsin x . 1) y sin –1(3x) 2) y cos–1(x) - 5) y 3 arccos(2x-4) 6) y tan –1(x-1) 8) y 3 cos–1 (x-2) 9) y - 2 1 tan–1 (x-1) 4 3) y arc sin (x 1) 7) y – arc sin x 10) 4) y 2 sin –1 ( x ) 3 2 y cot–1 x 1 7

Writing Trig Equations WS #1 1) 2) 3) 4) 5) 6) 7) 8) 8

Writing Trig Equations WS #2 1) 2) 3) 4) 5) 6) 7) 8) 9

Graph one cycle and fill in the blanks. 1 1. y Period sec 2 x 1 2 2 Equation of Asymptotes Three Specific Asymptotes 2. y 3cot x 6 1 Period Equation of Asymptotes Two Specific Asymptotes 3. y Period 2csc 2x 1 Equation of Asymptotes Three Specific Asymptotes 10

4. y 3 tan x 2 6 Period Equation of Asymptotes Two Specific Asymptotes Write the equation for each graph. 5. Equation: 6. Equation: 11

Evaluate. 2 7. cos 3 8. tan 10. cot 2 3 13. cos 5 5 sin sin cos 6 4 6 4 14. cos 3 7 cos 4 6 5 4 9. sin 5 6 12. sec3 11. csc sin 5 3 3 7 sin 4 6 7 3 4 15. 7 1 tan tan 3 4 tan tan If 0 in radians that make each statement true. 2 , determine the values of 3 16. cos 17. tan 18. csc 3 2 2 19. cot 2 1 3 20. sec2 4 3 21. csc2 2 12

Notes on graphing inverses of sine and cosine graphs 1st Graph y sin x 2 nd Interchange the values in the ordered pair and sketch in the graph below: angle value angle 3rd graph y value Sin 1 ( x) angle value Part 2 ) Do the same as above but to the graph y cosine x 1st Graph y cos x 2 nd Interchange the values in the ordered pair and sketch in the graph below: angle value angle 3rd graph y Cos 1 ( x ) value angle value 13

1st 2 nd Interchange the values in the ordered pair and sketch in the graph below: Graph y tan x angle value angle 3rd graph y tan 1 ( x) value angle value Part 2 ) Do the same as above but to the graph y cosine x 1st Graph y cot x 2 nd Interchange the values in the ordered pair and sketch in the graph below: angle value angle 3rd graph y Cot 1 ( x) value angle value 14

INVERSE TRIG FUNCTIONS PROBLEMS NOTES TWO GROUPS BASED ON SIMILAR RANGE y sin 1 x [ y tan 1 x ( y csc 1 x [ 2, 2 2 ] 2, 2 ) 2, 2 ] , y 0 2 Sample Problems 3 5 Reference Triangles 3 ex 1 sin(arctan( ) 2 cot(sin 1 ( 10 )) 10 sec(arc tan 3x) Angle Problems 4 sin 1 ( 3 ) 2 5 arc tan(-1) 6 arcsin(tan 3 ) 4 SECOND GROUP y cos 1 x [0, ] y sec 1 x [0, ] y cot 1 x (0, ) y 2 0 15

Sample Problems Reference Triangles 3 3 5 ex 1 sin(arccos( ) ) 2 sin(cos 1 ( 10 )) 10 sec(arc csc 3x) Angle Problems 4 cos 1 ( 3 ) 2 5 arc cot(-1) 6 arcsin(cos 3 ) 4 Summary of quadrant locations for inverse functions. 16

Examples: Find the exact values without using a calculator. 1. sin 1 1 3. sin 1 1 2 5. tan 1 7. Arc csc 2 9. sec 1 2. 4. cos 3 2 1 1 2 A rccos 6. csc 1 2 3 8. sec 1 2 10. A rc cot 1 3 1 2 12. A rcsin sin 7 6 14. sin 3 2 Find the exact value: 11. sin A rccos 13. Arc sec sec 15. sin cos 1 3 4 16. cos A rcsin 17. tan sin 1 1 2 18. sin tan 1( 1) 19. cos cot 1 20. cos A rcsin 21. sin Arc cos 3 4 22. csc cos 23. Arccot(-1) 24. cot 4 12 5 1 1 sin 4 1 2 7 5 13 2 9 3 17

Mon., Nov 12th Inverse Angles and Values Day 1 Packet plus text p. 350 # 59-64 Tue., Nov 13th Inverse Values and Angles Day 2 Worksheet Wed., Nov 14th QUIZ Sec 4.3 in text Assignment Packet p. 17 plus review Thurs., Nov 15th Review Game Study for Test Fri., Nov 16th Test over 4.3,4.6,4.7 No Homework