Summer Honors Work Packet. Course Title: Honors Trigonometry/Pre-Calculus. Teacher: Mr. Fochtman and Mr. Thayer

Transcription

1 Summer Honors Work Packet Course Title: Honors Trigonometry/Pre-Calculus Teacher: Mr. Fochtman and Mr. Thayer Contact Information: rfochtmanbwschools. net; dthayer(bwschools. net; Please Note: The summer assignment will be posted on the district website under a Summer Assignments Weebly Tab. This assignment will also be posted before that under the summer assignments tab at and at Estimated Time for Completion (Approximate): 6-8 Hours Objectives: We Will : * Solve applied problems relating to key geometry concepts; * Solve right triangles using the six basic trigonometric functions; * Convert between degrees and radians for a given angle; * Solve applied problems using the unit circle; * Find exact values of trigonometric functions; * Analyze coordinates of angles that are drawn in Standard Position; * Graph linear systems; *Solve quadratic equations and find the six trig functions for these angles Description of Activity: Students will solve applied problems using the above objectives/learning targets. Students will complete a pre-test consisting of multiple choice and short answer questions relating to the Big Ideas of Chapter 4 in Honors Trigonometry. These topics will also relate to Chapter P and Chapter 1 of the Pre-Calculus component of the course. These types of questions will appear on the first larger Unit Exam of the year by the end of the first weeklmiddle of the second week of school. Method(s) of Assessment: Students will complete this pre-test. We will clarify some of the questions by having students present some of their solutions the first week of school and using in-class discussions/questioning strategies. Impact on 1st Quarter Grade: This assignment will involve a 50 point grade for homework that will be included in the 1st Quarter Grade. We will also take a Point exam on this material that will contribute to nearly a ¼ of the first nine weeks grade. This pre-test corresponds to the learning targets in Chapter 4, which forms the foundation of everything that we do in Honors Trig/Pre-Calculus. Due Date: This assignment should be completed and returned to your instructor on the first day of school. The exam on all of this material will tentatively occur the second week of school. Do not procrastinate by waiting until the last week of summer to complete this assignment!!

2 Honors Trig/Pre-CaIc Summer Assignment 2014 Name: Date: 1. In right triangle ABC, if rnlc 90 and sina 4, cosb is equal to A. 4 B. 4 c. 4 D Which equation can be used to find the value of x in the right triangle shown? v 12 I x A. cos20 = B. sin20 = C. cos20 =_ D. cos70 = 12 x x in the accompanying diagram of right triangle ABC, LC is a right angle. Which equation is valid for ABC? A. cosa=- B. C. D. b a c b tana sina= cosb B 4. In the accompanying diagram. what is sine? A. 4 B. 4 C. 4 D. 4 K F 4 0 page 1

3 5. In the accompanying diagram of right triangle ABC, LB is a right angle, AB = 8, BC = 15, and C A = 17. A S B What ratio is equal to A. sina B. sinc C. cosc D. tana 6. In the right triangle shown in the diagram below, what is the value of x to the nearest whole nwnber? x 24 A. 12 B. 14 C. 21 D In the accompanying diagram of circle 0, are the coordinates of B? COA is a diameter, 0 is the origin, Oil I, and rnlboa = 30, What A. (, ) B. (, ) c. (, ) D. (, ) ii page 2 Honors Trig/PreCaIc Summer Assignment 2014

4 8. In the accompanying diagram of circle 0, point 0 is the origin, Y0 i, JO = I, and TOY is a diameter. If the coordinates of point.i are (4, 4). how many degrees are in the,nljoy? 9. Express radians in degrees. 10. Express in degree measure an angle of radians. II. What is the number of degrees in an angle whose radian measure is A. 150 B. 165 C. 330 D Which expression is equivalent to sin( 120 )? A. sin 600 B. sin 60 C. cos 30 D. sin Which is equal in value to sin 180? A. tan45 B. cos90 C. cos0 0. tan9o 14. Which expression is equivalent to sin 1500? A. cos30 B. sin30 C. sin( 30 ) D. sin30 page 3 Honors Trig(Pre-CaIc Summer Assignment 2014

5 15. The expression sin 240 is equivalent to A. sin 60 B. cos60 C. sin60 D. cos If tana =. what is the measure of LA to the nearest degree? A. 79 B. 60 C. 30 D If sin 43 =, what is the value of v to the nearest tenth? 18. The value of sin is B The value of sin( 210 ) is B.- C.1 page 4 Honors TrigIPre-Calc Summer Assignment 2014

6 Algebra 2 Name Trig Summer Assignment 2014 Date Period Find the value of each. Round your answers to the nearest ten-thousandth. 1) sin 66 2) tan 30 3) tan 18 4) tan26 Find the value of the trig function indicated. 5) coso 6) sing 7) sin 8) sin 9) cos 0 10) cos 9 5 I 9 11) tang 12) coso 2 Solve each equation by completing the square. 13)p 2 8p 96=0 14)k 2 4k 60=0 15)n2+4n 60=0 16)x2+12x+16=0

7 2±8x-54= 6 17)x 1)nH-2n 47=7 2 4m 7= 1O 20)r 19)m 2+16r+11= 4 21) b2 19b ) v2 13v+21 = 9 Solve each equation by factoring. 23)a2= 7a 10 24)n2= 3n+18 25)k2+24= lok 26)x2+12= 8x 27) 5n n+24=O 28) 7x 16x 15=0 29) 5m 27in + 28 = 0 30) 5x 2 + x 4 = 0 Factor each completely. 31) lox 2 +4x 10 32) 7rn 3 25x 2 +21m 24 3 Sm 33) 24p 3 8p 2 9p+3 34) 3n _5,12 +24n )a ),n4+14,n 37) x4 x ) x4 +3x ) 35x ) 20m x m ) 125x 4 3x 41) 10x x ) 27 u 43) 125x

8 -ii _ J_ -- 35) 64w ) x Divide. 47) (3m 3 +34m 2 +83m-f-29) (m 8) 48) (10r 3 28r 2 +2r 14) (r 3) 2 36x+36) (x+7) 49)(x3+x 50) (6n 3 52n 2 +69n+6) (n 7) Sketch the graph of each line. 51) 2x y=o 52) 2x+3y=6 V V V I 4 5 x

9 Sketch the graph of each linear inequality. 53) y3 54) v < 5 V 4 4 -: Identify the vertex and axis of symmetry of each. Then sketch the graph. 55) y x 1Ox 25,V ) y= x+ x V o 4 2 x -- - zzz:z - zz v Solve each system by graphing. 57) y=x 3 58) v=x 2 y = 3x + 1 y = x +4

10 - -2 Sketch the solution to each system of inequalities. 59) y5+1 y> --x-3 60) v>4x 1 y <x +2 Ày V $ H 1 Find the missing side of each triangle. Leave your answers in simplest radical form. 61) 8 cm 62) 5m/.V S 10 mi 63) in 64) 6 in 15 in S

11 65) 2J3 cm cm x State if each triangle is a right triangle. 66) 67) 12 km km 14 mi 4 km Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth. 68) // ///\ 69) Find the missing side Lengths. Leave your answers as radicals in simplest form. 70) 71) //\ 72) 2 73) -V

12 74) 75) 72