Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Approximations of π wikipedia , lookup

Perceived visual angle wikipedia , lookup

Trigonometric functions wikipedia , lookup

Transcript
```Unit 6 Trigonometry
Review Problems
PreCalculus 6-R
Review Problems
1
Review Problems
2
Review Problems
3
-1
1
Review Problems
4
Find the degree measure of the angle:
12°
Find the degree measure of the angle:
-450°
Review Problems
5
• To measure the speed of a current, scientists place a paddle
wheel in the stream and observe the rate at which it rotates. If
the paddle wheel has radius 3.2 m and rotates at 100 rpm, find
the speed of the current in m/s.
33.51
Review Problems
6
• Find sin a and cos B if x = 4, and y = 1.
sin a = ,
cos =
Review Problems
7
• What is the side labeled x equal to, if y = 22?
11
Review Problems
8
• Find x correct to one decimal place.
28.9
Review Problems
9
• The angle of elevation to the top of a particular
skyscraper in New York is found to be 12°
from the ground at a distance of 1.3 mi from
the base of the building. Using this information,
find the height of the skyscraper.
1459 ft
Review Problems
10
• A man is lying on the beach, flying a kite. He
holds the end of the kite string at ground level,
and estimates the angle of elevation of the kite
to be 55° . If the string is 470 ft long, how high is
the kite above the ground?
385 ft
Review Problems
11
• A water tower is located x = 350 ft from a building (see
the figure). From a window in the building it is
observed that the angle of elevation to the top of the
tower is 39° and the angle of depression to the bottom
of the tower is 25° . How tall is the tower (t)? How high
is the window (w)?
t = 447 ft;
w = 163 ft
Review Problems
12
• When the moon is exactly half full, the earth, moon,
and sun form a right angle (see the illustration). At that
time the angle formed by the sun, earth, and moon is
measured to be 89.75 . If the distance from the earth
to the moon is 235000 mi, estimate the distance from
the earth to the sun.
53,858,204 mi
Review Problems
13
• From a satellite 500 mi above the earth, it is observed
that the angle formed by the vertical and the line of
sight to the horizon is 60.276 . Use this information to
find the radius of the earth.
3300 mi
Review Problems
14
• A winch of radius 3 ft is used to lift
heavy loads. If the winch makes 7
revolutions every 15 s, find the speed
at which the load is rising.
8.796
Review Problems
15
correct to five decimal places.
31.40177
Review Problems
16
correct to five decimal places.
31.72546
Review Problems
17
• Find x correct to one decimal place.
108.9
Review Problems
18
• A 66-ft tree casts a shadow that is 110 ft long.
What is the angle of elevation of the sun?
31.0°
Review Problems
19
• An airplane is flying at an elevation of 5900 ft, directly
above a straight highway. Two motorists are driving
cars on the highway on opposite sides of the plane,
and the angle of depression to one car is 52 and to
the other is 51 . How far apart are the cars? Please
round the answer to the nearest foot.
9387 ft
Review Problems
20
• Evaluate the expression without using a calculator.
0
Review Problems
21
•
•
•
•
Solve the right triangle.
(a) Find b. Please give the answer to two decimal places. 30.03
(b) Find r. Please give the answer to two decimal places. 41.75
(c) Find .
44°
Review Problems
22
•
•
•
•
Solve the right triangle.
(a) Find a. Please give the answer to two decimal places. 13.53
(b) Find b. Please give the answer to two decimal places. 41.66
Review Problems
23
•
•
•
•
Find the exact value for each trigonometric function.
(a) sec 120° –2
(b) tan 390°
(c) cos 315°
Review Problems
24
To estimate the height of a mountain above a level plain, the
angle of elevation to the top of the mountain is measured to
be 34 . One thousand feet closer to the mountain along the
plain, it is found that the angle of elevation is 37 .
Estimate the height of the mountain. Please round the
6430
Review Problems
25
An airplane is flying at an elevation of 5900 ft, directly above
a straight highway. Two motorists are driving cars on the
highway on opposite sides of the plane, and the angle of
depression to one car is 52 and to the other is 51 .
How far apart are the cars? Please round the answer to the
nearest foot. 9387
Review Problems
26
Simplify the following trigonometric expression
tan x
sin 2 x
Review Problems
27
Simplify the following trigonometric expression
tan x cos x csc x
1
Simplify the following trigonometric expression
sin(z) + cos(–z) + sin(–z)
cos z
Review Problems
28
Simplify the following trigonometric expression
1
Simplify the following trigonometric expression
cos B + sin B tan B
sec B
Review Problems
29
Simplify the following trigonometric expression
cos 2 x
Simplify the following trigonometric expression
(1 – cos 2 x)(1 + cot 2 x)
1
Review Problems
30
Simplify the following trigonometric expression
sin 2 t + cos 2 t + tan 2 t
sec 2 t
Simplify the following trigonometric expression
sec A
Review Problems
31
Simplify the following trigonometric expression
2 csc x
Simplify the following trigonometric expression
cot x
Review Problems
32
Simplify the following trigonometric expression
sin 2 x
Simplify the following trigonometric expression
tan 2 t
Review Problems
33
1.
2.
3.
1
4. -1
-450°
5. 12°
6. 33.51
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
11
28.9
1459 ft
385 ft
t = 447 ft;
w = 163
53,858,204 mi
3300 mi
8.796
31.40177
31.72546
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
108.9
31.0°
9387 ft
0
30.03
13.53
41.75
44°
41.66
–2
6430
9387
tan x
sin 2 x
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
1
cos z
sec B
1
cos 2 x
1
sec 2 t
sec A
2 csc x
cot x
sin 2 x
tan 2 t