Math 171 Group Worksheet over Trigonometry (1.4)
January 21, 2016
Credit given for work shown.
Name
1. Convert the following angles to degrees or radians. Give exact answers.
(a) 3π/5 =
degrees
(b) 275◦ =
radians.
2. If π/2 ≤ θ ≤ 3π/2 and tan θ = 32 , find
cot(θ) =
sin(θ) =
csc(θ) =
cos(θ) =
sec(θ) =
3. Draw and label all sides and angles (in radians) of the two common right triangles.
(Hint: In degrees, they are the 30/60/90 and the 45/45/90 triangles.)
4. Find all solutions of the equations on the domain [0, 2π].
√
3
b) tan(x) = − √13
a) cos(x) =
2
cos(x + y) = cos x cos y − sin x sin y
sin(x + y) = sin x cos y + cos x sin y
π
+
5. Use the addition formula (above) to compute cos 2π
3
4 exactly.
6. Find all solutions to cos(x) − sin(2x) = 0 in the interval [0, 2π]. (Hint: Use formula above.)
7. From the third story of a building (50 feet) David observes a car moving towards the building
driving on the streets below. If the angle of depression of the car changes from π/6 to π/4
radians while he watches, how far did the car travel?
8. If the latitude of a location is known, then the following formula can be used to calculate the
angle of inclinations of the sun on any given date of the year:
360
θ = 90◦ − L − 23.5◦ cos (N + 10) 365
where θ is the angle of sun, L is the latitude and N represents the number of the day of the
year that corresponds to the date of the year. [Note: This formula is accurate to 0.5◦ .]
(a) What is the amplitude?
(b) What is the period?
(c) Bozeman is location at a latitude of N 45.677890◦ . What is the angle of the sun today?
(d) What day of the year is the sun the highest in the sky? What day is it the lowest?
9. A surveying crew is given the job of verifying the height of a cliff. From point A, they measure
an angle of elevation to the top of the cliff to be α. They move 507 meters closer to the cliff
and find that the angle to the top of the cliff is now β. How tall is the cliff in terms of α and
β?