Download Algebra II BC

Alg 2 BC U13
Day 9 - Review
1. Given csc  4 / 3 and cos  0 , find the values of the other 5 trig functions USING IDENTITIES.
Match each trigonometric expression to one of the following.
a) cscx
b) tanx
c) sin2x
d) sinxtanx e) sec2x
3. cos2x(sec2x -1)
2. sinxsecx
4. sec4x – tan4x
f) sec2x + tan2x
6. (sec2x – 1)/sin2x
5. cotxsecx
Verify each identity.
1  csc x
 sec x
7.
cot x  cos x
9. tan 4 x  tan 2 x sec2 x  tan 2 x
8.
cot 2 x
1  sin x

1  csc x
sin x
10. 2sec2 x  2sec2 x sin 2 x  sin 2 x  cos 2 x  1
Solve each equation for 0 ≤ x < 2π. (Use a calculator for 15 -17 only.)
11. 2sin 4 x  sin 2 x
12. sec x  tan x  1
13. 2 cos 2 x  1  cos x
14. 2 tan 2 x sin x  tan 2 x  0
15. 5sin x  3  1
16. 2 tan 2 x  5 tan x  3  0
17. 6 cos 2 x  2 cos x  1
Solve each problem. Round answers to 3 decimal places.
18. A flagpole is mounted on the roof of the library. From a point 100 feet away, the angles of elevation to the
base of a flagpole and the top of the flagpole are 28° and 39°45’ respectively. Find the height of the flagpole.
19. A researcher is taking pictures of puffins who are on the edge of a cliff. To find the height of the puffins
above the water, she measures a 28 degree angle of elevation from her line of sight to the puffins. If her camera
is 15 feet above the water, and 40 feet horizontally from the cliff, how high above the water are the puffins?
20. From the top of a 150 ft. building Flora observes a car moving along toward her. If the angle of depression
of the car changes from 18 degrees to 42 degrees during the observation, how far does the car travel?
Some extra verifications if you are interested:
 csc x  1
 sec x
21.
cos x  cot x
22.
cot 3 x
 cos x(cot 2 x)
csc x
23.
sin 2 x  (1  sin 2 x) tan 2 x
24.
cos 2 x
 sin x  csc x
sin x
25.
1
1

1
sin x  1 csc x  1
26.
cot 2 x(sec2 x  1)  1
And some more problems if you want:
Use the Fundamental IDs to find the requested trig value.
3
, x Quadrant I, find cot x .
4
2
2.) Given sin x  , 90° < x < 180 °, find cos x .
3
1
3.) Given cos x  , 32  x  2 , find tan x .
8
Simplify the following.
1.) Given tan x 
4.)
1  tan 2 x
1  cot 2 x
5.) sin x(cot x  csc x)
6.) csc x tan x cos x
7.)
sin 2 x  cos 2 x
cos 2 x
Verify the following. Don’t forget REASONS for each step!
8.) cos 2 x csc x sec x  cot x
1  cos 2 x
9.)
 sin x cos x
tan x
10.) tan x(sin x  cot x cos x)  sec x
11.) sec4 x  tan 4 x  1  2 tan 2 x
12.)
1  sin x
 sec x  tan x
cos x
13.) sin 3 x  sin x  cos 2 x sin x
Answers to front:
sin   
1.
3
4
sec  
7
cos  
4
14. x  0,  ,
4 7
7
6
,
6
15. .927, 2.214
7
cot   
3
16. 1.249, 2.678, 4.391, 5.820
3 7
tan   
7
2. b
 5
17. .918, 5.365, 1.849, 4.435
3. c
4. f
5. a
6. e
18. 29.998 feet
19. 36.268 feet
20. 295.061 feet
11. x  0,  ,
 3 5 7
, , ,
4 4 4 4
12. x = 0
13. x 
4 3
3
3.) 3 7
4.) tan 2 x
6.) 1
7.) sec 2 x
1.)
 5
3
Answers to back:
,
3
,
2.) 
5
3
5.) cos x 1