Practice Questions Exam 2 - Plane Trigonometry | MATH 111, Study notes of Trigonometry

Download Practice Questions Exam 2 - Plane Trigonometry | MATH 111 and more Study notes Trigonometry in PDF only on Docsity! Math 111 - Trigonometry Practice Exam 2 Warning: This study guide is not all inclusive- there may be material on the test which is covered in the book but not here. This is simply meant to be a supplemental study aid to the homework and class notes 1. Graph two periods of y = −2 + 4 cos(π(x − 2)). Find the amplitude, period, and average value. Label the axes in a way to reflect the important characteristics of the graph (i.e. when the function reaches it maximum, minimum, and average value). 2. Below is a data table for a function involving a trigonometric function. x -1 0 1 2 3 4 y 3 7 11 7 3 7 Determine a possible formula for the trigonometric function. 3. Consider a function with the below graph: -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 1 2 3 (a) Find a formula for this function involving sine. (b) Find a formula for this function involving cosine. 4. Find the following exact values (a) The period of the function y = tan(4(x− 3)) (b) The horizontal shift of the function f(x) = 1− 2 sin(3(x− 4)) (c) The average value of the function g(x) = 2− 2 cos(π(x+ π)) (d) tan(cos−1(− 5 13 )) (e) cos(arctan( √ 3) + sin−1(1 3 )) (Hint: Use the Cosine of a Sum identity) (f) sin(tan−1(3 2 )) 5. Mark the following true or false. (a) csc(−x) = − csc(x) (b) The amplitude of y = −3 sin(5(x+ 3)) is −3. (c) arctan(z + 3) = arctan(z) + 3 (d) tan−1 x = arctanx 6. For each of the below expressions, determine if the statement is possible or impossible. For those that are possible, determine the exact value. Represent all angles in radians. (a) arcsin π (b) cos−1(− √ 3 2 ) (c) sin(−4) (d) sin−1(30◦)