Precalc -Trig homework due in 5 hours

Name: _____________________________

MTH129 F2018 - A PI

Show all work neatly on paper provided. Label all work. Place final answers on the answer sheet.

1. Find the radian measures of the angles with the given degree measures.

a) 81° ________________ b) 36° ________________

Find the degree measures of the angles with the given radian measures.

c) 13𝜋

6 ________________ d)

5𝜋

27 ________________

2. a. Find all 6 trigonometric values of t if cos 𝑡 = − 5 13⁄ and the terminal point to t is in quadrant III

Place answers in space below formulas

b. Find the reference number for 𝑡 = 2𝜋

3 2b ________________

c. 𝑃 ( √3 2 ⁄ , 𝑦) is on the unit circle and in quadrant IV. Find the y coordinate. 2c ________________

3a. Find the length s in the given figure

3a ________________

3b. Find x correct to one decimal place.

3b x = ________________

4. a. From the top of a 300 foot light house, the angel of depression to a ship in the ocean is 17°. How far is the

ship from the base of the lighthouse? ________________

4b. A 40 foot ladder leans against a building. If the ladder is 6 feet from the base of the building, what is the

angle measure formed by the ladder and the building? ________________

5. Use the Law of Cosine and the Law of Sine to find the remailing parts of the triangle:

𝛽 = 53.5°; 𝑎 = 9; 𝑐 = 12.5

__________________ _____________________ ______________________

6. The area of the sector of a circle with an angle of 45° is 2 square feet. Find the radius of the circle.

______________________

BONUS: Looking at the given right triangle, find the measure of angle x_________________

FORMULAS

𝑎2 + 𝑏2 = 𝑐 2 𝑥 2 + 𝑦 2 = 1 𝑠𝑖𝑛2𝜃 + 𝑐𝑜𝑠2𝜃 = 1 SOH CAH TOA

𝑆 = 𝑟𝜃 𝐴 = 1

2 𝑟2𝜃

𝑎2 = 𝑏2 + 𝑐 2 − 2𝑏𝑐 𝑐𝑜𝑠𝛼 𝑠𝑖𝑛𝛼

𝑎 =

𝑠𝑖𝑛𝛽

𝑏 =

𝑠𝑖𝑛𝛾

𝑐

2a ________________ ________________ ________________

________________ ________________ ________________

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