PRE CALCULUS EXAM 4

Name:

109-11 Unit 4 Exam Draw diagrams and show all work. Calculators are permitted but approximations are not valid when the question calls for exact values.

1. If ( √3

2 ,

1

2 ) is a point on the unit circle corresponding to angle 𝜃, find the exact values of

each of the six trigonometric values of 𝜃 in simplest terms. 2. Convert 210° to radians. 3. Find a positive angle less than 2𝜋 which is coterminal with the angle 29𝜋/6.

4. Find the lengths of all sides (approximate to the nearest hundredth when necessary) and the measures of all angles (in degrees) for the right triangle below:

5. Graph the function 𝑦 = 3 sin(2𝑥 – 𝜋/4).

50°

11

6. Verify the identity:

1−cos 2𝑥

sin 2𝑥 = tan 𝑥

7. Solve the triangle with sides 𝑎 = 6 and 𝑏 = 4 and included angle 𝛾 = 96°. 8. The triangle with sides 𝑎 = 20 and 𝑏 = 26 and angle 𝛼 = 39° is an ambiguous case.

Solve both triangles.

9. A surveying team is on a mission to confirm the estimated altitude of a mountain on an island in the central Pacific. (There are worse jobs in this world.) One of the team’s interns accidentally damaged their altitude-finding portable GPS unit, so they have to do this by hand. The team settles onto a comfortable point on the beach at sea level and sets up their precision inclinometer, which indicates an angle of 24.73° to the top of the mountain. They then measure off exactly 200 meters straight away from the mountain and take an inclination reading again; the angle to the peak from the new position is 22.85°.

Draw a diagram, set up a formula with the relevant function, and find the height of the mountain in meters. Assume that the gear which wasn’t damaged by the intern is highly accurate, disregard the minor influence of the curvature of the Earth, and round to the nearest hundredth of a meter.