Answers to 3rd 9 week review:
1. Convert 280˚ to radians:
2. Convert
to degrees: 216˚
3. If sin θ = 5/6 find the remaining 5 trig functions. Write answers as fractions
cos θ =
, tan θ =
, csc θ = 6/5, sec θ =
, cot θ =
4.
4. Use reference angles to find the following; (will always be a 30, 45, or 60˚ angle)
a. cos 420˚= cos 60 = 1/2
b. sin
= sin 225 = (45˚ reference angle) =
c. tan
= tan 480 = tan 120 (60 reference angle) =
5. Use quadrantal angles to find the sin, cos, and tan when (will always be at 0, 90, 180, 270, or 360)
a. θ = -270˚: sin -270 = 1, cos -270 = 0, and tan -270 = Ø
b. θ = 3 : 3
sin 3 = 0, cos 3 = -1, and tan 3 = 0
6. Given (2, 8) use the terminal side to find all 6 trig functions
sin =
, cos =
, tan = 4, csc =
7. Find the exact value of without a calculator
a. sin 225˚:
b. cos
:
c. tan 90˚: Ø
d. csc :
e. sec
f.
:
cot 180˚: Ø
, sec =
, cot = 1/4
8. find x to the nearest tenth
tan 36 =
, 15tan 36 = x, x = 10.9
sin 25 =
25 ÷ sin 25 = x, x = 59.2
9. A tree casts a 45 foot shadow. If the sun is at a 30˚ angle of depression, how tall is the tree?
tan 30 =
, 45 tan 30 = x, x = 25.99 or 26 feet
10. A guy-wire is attached to a 150 foot tower. The angle of elevation that the guy-wire makes with the ground is 15˚
How long is the guy-wire.
sin 15 =
, 150 ÷ sin 15 ≈ 580 ft
11. Two markers A and B on the same side of a canyon rim are 56 ft apart. A third marker C, located across the rim, is
position so that
= 72˚ and
= 53˚. Find the distance between C and A
Use the law of sin to find AC:
, 56 sin 53 = b sin 55, b = 54.6 or 55 feet
12. Graphing. Determine the amplitude, period, frequency, phase shift, and vertical shift.
a. f(x) = 2sin (3x – 2) + 3:A = 2, P =
,F=
, PS =
b. f(x) = -1/2 cot (x + 3) – 2: A = ½, P = 2 , F =
, VS = 3
, PS = 3, VS = -2
13. graph: plug into calculator to see what the graph looks like, make sure you are in radians
a. f(x) = sin x
b. f(x) = cos x
c. f(x) = tan x
14. find the exact values of:
a. sin-1 (
:
b. arccos (
c. sin -1(tan
:
d. tan (cos-1(1/2)):
15. Use the law of sines to find all missing sides and angles
A: 26 sin A = 34 sin 28: 38˚
C: 180 – 38 – 28 = 114
c: 26 sin 114 = c sin 28: 50.6
16. Use the law of cos to find all missing sides and angles
a: a2 = 152 + 182 – 2(15)(18)cos 105, a = 26.2
B: 152 = 26.22 + 182 – 2(26.2)(18) cos B: 34˚
C: 180 – 34 – 105 = 41˚
17. Find the area of the triangle
A = ½ (15)(8)sin 56 = 37.3