please help me answer these questions and please consider the expectations as well also please show steps so I understand. Thank youu

MODULE 5: Lesson 1 ASSIGNMENT Lesson 1: The Tangent Function The Module 5: Lesson 1 Assignment is worth 8 marks. The value of each question is stated in the left hand margin. (1 marks) 1. Depending on the problem, it can be difficult to figure out which trigonometric function you should use. When should you use the function tan 6 , compared to the sin 6 or cos 6 functions? 2. A drag strip is 404 metres long. Suppose a set of bleachers 3m deep are set up 20 m away from the track. (2 marks) a. Which position in the bleachers requires you to turn your head farthest away from a straight-forward position to watch the race? What is the greatest angle required for this seat, to the nearest hundredth? Mathematics Booklet 5 (2 marks) b. Suppose you are sitting in the front middle seat. Write an equation that represents distance, d, of the track visible by turning your head an angle of 0 in one direction. Include the domain for this scenario. 3. The function f(0) = tan 0 has the following transformations performed on it, a vertical stretch of 2 about the x-axis, horizontal stretch of 3 about the y-axis, vertical translation of 2 units down and a horizontal translation of 3 units to the left. (1 mark) a. Determine the equation of the transformed function g(0).. (2 marks) b. Determine the non-permissible values of the new transformed function. Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 1 on Moodle. Now go to Lesson 2 on Moodle.MODULE 5: Lesson 2 ASSIGNMENT Lesson 2: Equations and Graphs of Trigonometric Functions The Module 5: Lesson 2 Assignment is worth 7 marks. The value of each question is stated in the left hand margin. 1. The path of a swing could be modeled by the function h(t) = 15 cos (zz"t) + 65, where his the height in centimeters above the ground and t is the time in seconds. (1 mark) a. What is the maximum height of the swing? Determine using only the amplitude and midline. (1 mark) b. How many seconds does it take to reach minimum height? Use the period and your knowledge of the cosine function to determine this and show your calculations and/or explain in words your reasoning. (2 marks) c. Determine the height of the swing after 10 s have passed, algebraically. Round your answer to the nearest tenth. (3 marks) d. For how many seconds within one cycle is the swing less than 60 cm above the ground? Round your answer to the nearest tenth of a second. Solve this question graphically & explain in words. Expectations O The graphs are labeled, scale provided, key points labeled O Written explanation of how answer was obtained Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 2 on Moodle. Now go to Lesson 3 on Moodle. MODULE 5: Lesson 2 ASSIGNMENT T UIT VIUUuTe: MODULE 5: Lesson 2 ASSIGNMENT MODULE 5: Lesson 3 ASSIGNMENT Lesson 3: Trigonometric Identities The Module 5: Lesson 3 Assignment is worth 4 marks. The value of each question is stated in the left hand margin. escx (2marks) 1. Determine the non-permissible values for the expression T canx (2marks) 2. Simplify the following expression to a single trigonometric function. tan(x)(lsin4(x))sec(x) 1sin'(x) cot(x) Expectations [ You are always expected to check for and list any non-permissible values before simplifying. The question does not have to ask you to do this, itis an assumed expectation. Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 3 on Moodle. Now go to Lesson 4 on Moodle. (3 marks) 3. Algebraically determine the general solution to the equation cos 2x = cos x . Express your answers in 7t radians. Expectations O When using identities, itis a requirement to only use identities on your diploma given formula sheet Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 4 on Moodle. Now go to Lesson 5 on Moodle. MODULE 5: Lesson 5 ASSIGNMENT Lesson 5: Proving Trigonometric Identities The Module 5: Lesson 5 Assignment is worth 8 marks. The value of each question is stated in the left hand margin. (2 marks) 1. Given the identity, 1 + cot'x = csc'x. For which values of x is the proof valid? Mathematics 2. Prove each identity. Show your steps and/or explain your reasoning. sin x sin x 3 marks) a. 1+sin x 1- sin x - =- 2tan x Expectations O When using identities, it is a requirement to only use identities on your diploma given formula sheet O When proving identities, you are expected to check and list any non-permissible values before simplifying O When proving an identity, you are not permitted to move values across the equation, or multiply both sides of the equation by a value. You are only allowed o rewrite, substitute identities, or simplify expressions on one side of the equation at a time. When proving an identity, you need to how each full step at a time When you have finished proving an identity, you need to write a concluding statement. This can be LS = RS, or QED.(3marks) b.sin@tan + cos sec + 1 = sec'0 cos\" @ Expectations [ When using identities, itis a requirement to only use identities on your diploma given formula sheet [J When proving identities, you are expected to check and list any non-permissible values before simplifying. [J When proving an identity, you are not permitted to move values across the equation, or multiply both sides of the equation by a value. You are only allowed to rewrite, substitute identities, or simplify expressions on one side of the equation atatime. When proving an identity, you need to show each full step one at a time When you have finished proving an identity, you need to write a concluding statement. This can be LS =RS, or QED. Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 5 on Moodle. Be sure that you complete the Module 5 Summary as well. MODULE 5: Lesson 5 ASSIGNMENT