quizzes 5-7

Quiz 6 MATH 115 Fall 2019 SHOW ALL WORK to receive credit. 1. 5 pts. Solve, finding all exact solutions in radians, in [0, 2π). cos(x) sin(2x) = sinx

2. 4 pts. Solve, finding all exact solutions in radians, in [0, 2π). tan(3x - π/2) = -1

3. 5 pts. Solve the triangle(s), if possible. Round each final answer to the nearest hundredth. (Only round the final answers.) α = 36°, side a = 12, side b = 15 (Side a is opposite angle α. Side b is opposite angle β.)

4. 4 pts. Solve the triangle(s), if possible. Round each answer to the nearest hundredth of a degree. (Only round the final answers.) Side a = 24, side b = 10, side c = 18

For problem 5, use the bearings described on page 905 of Section 11.2 in the College Trigonometry textbook.

5. 5 pts. Island A is 50 miles north of Island B. At noon today, the bearing from Island A to the eye of a hurricane is S42°E. The bearing from Island B to the eye of the hurricane is S60°E. Determine the distance from Island A to the eye of the hurricane to the nearest tenth of a mile. (Draw the picture before you try the math!) (Only round the final answers.)

6. 7 pts. Round each final answer to the nearest hundredth. (Only round the final answers.)

Vector u is <8, -5> . Vector v is <-6, 1 >

6A. Find the vector u – v

6B. Find the magnitude of u – v

6C. Find the angle α that the vector u – v makes with the positive x axis. The angle α should be measured in degrees, rounded to the nearest hundredth of a degree.

6D. Find the dot product u∙v

6E. Find the angle θ between u and v. θ should be an angle measured in degrees, between 0° and 180°, rounded to the nearest hundredth.