ANALYTIC TRIGONOMETRY UNIT 7

VERIFYING IDENTITIES LESSON 7.1

PROOFS! I know, we have already done proofs. But… Now we are able to transform the left, right, or both sides of the equation to verify the identity. Watch out for conjugates, factoring, Pythagorean Identities, etc…when working on these proofs.

EXAMPLE:

HOMEWORK: Pages 498 – 499 #’s 1 – 47 odds

BELL WORK:

TRIGONOMETRIC EQUATIONS LESSON 7.2

EXAMPLE: Find the solutions for the equation sin θ = ½. How many solutions are there? How do we represent them?

EXAMPLE:

Solve the equation cos 2x = 0 and express the solutions in both radians and degrees.

EXAMPLE: Solve the equation sin θ tan θ = sin θ.

HOMEWORK: Page 511 #’s 1 – 13 odds

BELL WORK: Solve the equation 4sin² x tan x – tan x = 0 given the following restrictions: A) x is in the interval from [0,2π] B) x is any real number C) x < 0

EXAMPLE: Solve the equation 2sin²x – cos x = 1.

EXAMPLE:

HOMEWORK: Page 511 #’s 19 – 35 odds

BELL WORK:

EXAMPLE:

HOMEWORK: Pages 511 – 512 #’s 37 – 59 odds This assignment will be collected!!!

WORD PROBLEM:

HOMEWORK: Pages 512 – 513 #’s 68, 71, 73, 75b

BELL WORK:

BELL WORK CONTINUED:

BELL WORK: Simplify the expressions below (find the exact value) 1) cos 45° + cos 30° 2) cos(75°)

ADDITION AND SUBTRACTION FORMULAS LESSON 7.3

ADDITION/SUBTRACTION FOR COSINE

ADDITION/SUBTRACTION FOR SINE

ADDITION/SUBTRACTION TANGENT

COFUNCTION FORMULAS

HOMEWORK: Pages 522 – 523 #’s 5 – 9 odds, 17 – 21 odds,

BELL WORK: If a and b are acute angles such that the csc a = 13/12 and cot b = 4/3, find: 1) sin (a + b) 2) tan (a + b) 3) the quadrant containing a + b

EXAMPLES:

EXAMPLE:

Use the addition and/or subtraction formulas to find the solutions for the equation in the interval from [0,π]. sin4x· cosx = sinx· cos4x

HOMEWORK: Pages 523 – 524 #’s 10, 22, 26, 36, 38, 40

QUIZ FRIDAY Lessons 7.1 – Proofs 7.2 Solving Trigonometric Equations (either on a given interval or for all real numbers) 7.3 Addition/Subtraction Formulas and Proofs

PRACTICE PROBLEMS: Page 524 #’s 54, 55, 58

BELL WORK:

CLASS WORK: Pages 511 – 512 #’s 31, 34, 38, 42 Pages 523 – 524 #’s 20, 33, 38, 56 Also review the proofs from lesson 7.1!

BELL WORK: Use the addition and/or subtraction formulas to find the solutions for the equations in the interval from [0,2π]. 1) sin4x· cosx = sinx· cos4x 2) tan2x + tanx = 1 – tan2x· tanx

MULTIPLE-ANGLE FORMULAS LESSON 7.4

DOUBLE ANGLE FORMULAS

EXAMPLES:

EXAMPLE:

HALF-ANGLE IDENTITIES

EXAMPLES:

HOMEWORK: Page 532 #’s 3, 11, 15, 17, 23

BELL WORK:

EXAMPLES:

CLASS WORK: Pages 532 – 533 #’s 2, 4, 18, 20, 25, 35, 37, 40

HALF-ANGLE FORMULAS

EXAMPLES: Find the exact value of the sin 22.5°. Find the exact value of the cos 112.5°.

EXAMPLE:

HOMEWORK: Pages 532 – 533 #’s 5, 9, 13, 19, 25, 33, 35, 37

CLASS WORK/HOME WORK: Pages 532 – 533 #’s 4, 8, 10, 12, 16, 22, 24, 34, 36, 38

BELL WORK: Solve:

INVERSE TRIGONOMETRIC FUNCTIONS LESSON 7.6

LET’S REVIEW INVERSES:

GRAPH OF ARCSINE Let’s derive the graph of y = arcsin(x)

GRAPH OF ARCCOSINE Let’s derive the graph of y = arccos(x)

GRAPH OF ARCTANGENT Let’s derive the graph of y = arctan(x)

HOMEWORK: Pages 553 – 554 #’s 1 – 19 odds, 31 and 32

BELL WORK:

EXAMPLE:

GRAPHS OF OTHER INVERSES **Blue Chart on Page 552** These are the graphs for the inverses of cotangent, secant, and cosecant. We are going to skip these!!!

HOMEWORK: Pages 553 – 555 #’s 10 – 20 evens, 53, 55, 57

TEST WEDNESDAY Lessons 7.1 – 7.6 (no 7.5) Proofs Solving Trigonometric Equations (For all real numbers and through intervals) Addition and Subtraction Formulas Double/Half Angle Identities Inverse Functions(Sine, Cosine, and Tangent only)

TEST REVIEW: Pages 557 – 559 (Unit 7) #’s 1 – 8, 14, 18, 19, 23 – 34, 45, 48, 53, 56 Pages 620 – 623 (Unit 8) #’s 5 – 10, 40 – 45, 47, 48 As always, these are review problems that are very similar to problems that you will see on your test!!! Also remember to look over previous homework assignments!!!