Unit S Student Success Sheet (SSS) Trigonometric Identities Part 3 (section 5.5)
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1 Unit S Student Success Sheet (SSS) Trigonometric Identities Part 3 (section 5.5) Standards: Trig 11.0 Segerstrom High School -- Math Analysis Honors Name: Period: Thinkbinder Study Group: Reminders: Practice Problems (PQ & PT) are completed in spiral bound notebook only. All pages in spiral notebook should be labeled accordingly: Unit Concept - (title of assignment) Examples: Unit S Concept 1 Practice Quiz Unit S Concept 1-4 Practice Test Website with all video links and resources: kirchmathanalysis.blogspot.com Edmodo Group Codes for class communication: If you want to achieve excellence, you can get there today. As of this second, quit doing lessthan-excellent work. Thomas J Watson Concept Mandatory Practice 1 Writing products as sums Practice quiz 1 # What we will be learning 2 Writing sums as products Practice quiz 2 3 Using power-reducing formulas Practice quiz 3 4 using half-angle formulas Practice quiz 4 5 Finding function values with double angles and half angles Practice quiz 5 (right triangles) 6 Solving multiple angle equations (using multiple-angle Practice quiz 6 identities) 7 solving equations with half-angle formulas Practice quiz 8 Optional Extra practice from textbook We will conclude our study of trigonometric identities by looking at five more types of formulas: double-angle, halfangle, product to sum, sum to product, and power-reducing. Like last unit, these formulas expand our usage of the unit circle from the main angles of 0, 30, 45, 60, and 90 to many more.
2 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors---
3 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Writing products as sums 1. ; u= v= 2. ; u= v= Extra video #10 covers the following problems. Use these as extra practice and the videos as a guide if you need help Writing sums as products 1. ; u= v= 2. ; u= v= Extra video #11 covers the following problems. Use these as extra practice and the videos as a guide if you need help
4 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Using power-reducing formulas 1. cos4x= using power reducing formulas = = FOILing the numerator= Still not in the first power! Let m=2x ; therefore = Our whole equation of: now becomes: Now, we must make it look nicer make all of the numerator have a denominator of 2 = Add like terms in the numerator and multiply top and bottom by ¼ to get rid of the 4 in the denominator 2. Try it with sin 4 x=
5 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Extra video #8 covers the following problems. Use these as extra practice and the videos as a guide if you need help using half-angle formulas o ; u= ; u/2 is in quadrant, so sine is, cosine is 2. ; u= ; u/2 is in quadrant, so sine is, cosine is
6 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors o ; u= ; u/2 is in quadrant, so sine is, cosine is 4. ; u= ; u/2 is in quadrant, so sine is, cosine is Extra video #9 covers the following problems. Use these as extra practice and the videos as a guide if you need help
7 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Finding function values with double angles and half angles (right triangles) 0 to 90 Half angle - 0 to 45 still 1st quadrant! 90 to 180 Half angle - 45 to 90 1st quadrant! 180 to 270 Half angle - 90 to 135 2nd quadrant! = 270 to 360 Half angle to 180-2nd quadrant! 1. is in Quadrant II ; sin is positive = You are identifying the quadrant for the HALF ANGLE from the information they give you about the REAL ANGLE 2. Quadrant ; sin is 4. Quadrant ; sin is 3. Quadrant ; cos is 5. Quadrant ; tan is
8 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- 0 to 90 Double angle - 0 to in 1st or 2nd quadrant 90 to 180 Double angle -180 to 360 (3rd or 4th quadrant) 180 to 270 Double angle to 540-1st or 2nd quadrant 270 to 360 Double angle to 720-3rd or 4th quadrant 6. = 7. Quadrant ; 9. Quadrant ; 8. Quadrant ; 10. Quadrant ;
9 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Extra video #12 covers the following problems. Use these as extra practice and the videos as a guide if you need help Find the half angle and double angle values for all three trig functions (6 parts per problem). In addition, once you find the original three trig functions, find the reciprocal trig functions as well Find the half angle and double angle values for all three trig functions (6 parts per problem). In addition, once you find the original three trig functions, find the reciprocal trig functions as well Solving multiple angle equations (using multiple-angle identities) *Please note to graph, mode must be in radians! 1. algebraically 2. algebraically 3. graphically 4. graphically
10 ---Unit S Student Success Sheet--- Trigonometric Identities Part 3 (section 5.5)---Math Analysis Honors--- Extra video #13 covers the following problems. Use these as extra practice and the videos as a guide if you need help solving equations with half-angle formulas DON T FORGET TO CHECK FOR EXTRANEOUS SOLUTIONS ANYTIME YOU square both sides IN THE PROCESS OF SOLVING! Extra video #14 covers the following problems. Use these as extra practice and the videos as a guide if you need help See kirchmathanalysis.blogspot.com for answer key to most problems in this packet!
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