Question

1. Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The circle's radius is 2.2 units long and the terminal point is (−1.38,1.71)(-1.38,1.71). What is the Angle measure?

2.Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The terminal point is (2.42,−1.6)(2.42,-1.6). What is the angle Measure?

3. Savannah is skiing along a circular ski trail that has a radius of 2.6 km. She starts at the 3-o'clock position and travels in the CCW direction. Savannah stops skiing when she is 1.512 km to the right and 2.115 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Savannah's path.

a. How many radians has the angle swept out since Savannah started skiing?

radians   

b. How many km has Savannah skied since she started skiing? in km

4. Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".

1. Solve 6sin(θ)=16sin(θ)=1 for θθ (where 0≤θ<2π)

2. Solve 12sin(θ)=1212sin(θ)=12 for θθ (where 0≤θ<2π)

3. Solve 4sin(θ)=144sin(θ)=14 for θθ (where 0≤θ<2π)

Answer 1