**MATH 115 Quiz 5 Summer 2022**

1) Find the Amplitude of y = -3sin x

2) Find the period of y = 2cos(x + π/4).

3) Find the phase shift of y = -4 + 3sin(3x – π/6)**Using a calculator, solve the following problems. Round your answers to the nearest tenth.**

4) A boat leaves the entrance of a harbor and travels 26 miles on a bearing of N 10° E. How many miles north and how many miles east from the harbor has the boat traveled?

5) Two tracking stations are on the equator 150 miles apart. A weather balloon is located on a bearing of N35°E from the western station and on a bearing of N 25°W from the eastern station. How far is the balloon from the western station? Round to the nearest mile.

6) The distance from home plate to dead center field in Sun Devil Stadium is 402 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from third base to dead center field?

**Find the specified vector or scalar.**

7) **u** = <12, 3>, **v** = <-5, -3>; Find **u** + **v. **

8) **u** = <11, 4> and **v** = <7, -8>; Find** u **∙** v**. **Find the angle between the given vectors. Round to the nearest tenth of a degree.**

9) **u** = <7, 2>, **v** = <8, -4>** **

**Solve the equation on the interval [0˚, 360˚).**

10) (tan x – 1) (cos x – 2) = 0

11) Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle.

12) −2×2−36x−2y2−112=0