Trigonometry Homework

MATH 115 QUIZ 4 Section 6381 Summer 2020

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

NAME_____________________________

INSTRUCTIONS

· The quiz is worth 50 points total. There are five problems (each worth 10 points).

· You must show all work in order to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor.

· The quiz is open book and open notes . This means that you may refer to your textbook, notes, and online course materials, but you must work independently and may not consult anyone . The brief honor statement is on top of the exam. If you fail to put your name under the statement, your quiz will not be accepted. You may take as much time as you wish, provided you turn in your quiz via LEO by 11:59 pm EDT on Tuesday, June 30.

· The completed quiz should be uploaded to the Quiz 4 Assignment Folder as an attachment. Emailed quizzes and exams will not be accepted. Thank you for understanding.

1. Find the requested value:

(a) If with in Quadrant I, what is ?

(b) If with in Quadrant II, what is ?

(c) If with in Quadrant III, what is ?

(d) If with in Quadrant IV, what is ?

Show work and rationale, and simplify your answer for full credit. Answers based on technology (calculators, applets, software packages, etc.) are not accepted.

2. Find all of the angles which satisfy the equation: (Express your final answer in radian measure)

(a)

(b)

(c)

(d)

Show work and rationale, and simplify your answer for full credit. You may leverage the chart on page 724 of the textbook for a reference angle, which is also pasted here for your quick reference. Answers based on technology (calculators, applets, software packages, etc.) are not accepted.

3. Let α and β be two angles in unit circle. Given :

(a) Use sum identity to determine (4 pts)

(b) Use sum identity to determine (4 pts)

(c) Based on your answer from (a) and (b), what quadrant does angle belong to? Why? (2 pts)

Show work and rationale, and simplify your answer for full credit. Answers based on technology (calculators, applets, software packages, etc.) are not accepted.

4. Suppose Answer the following questions - Use the half angle formulas to solve for parts (b) and (c):

(a) What quadrant does the half angle belong to? (2 pts)

(b) Find . (4 pts)

(c) Find . (4 pts)

Show work, rationale and simplify your answers for full credit.

5. Graph at least one cycle of the given function using graphing calculator or other software and state the period, amplitude, phase shift and vertical shift of the function:

(a)

(b)

Show work and rationale, and label the x-axis and y-axis clearly for full credit.