Download ALGEBRA II Unit: Trigonometry Review Sheet

Name: ______________________ Date: ________
ALGEBRA II Unit: Trigonometry Review Sheet
1) Write the 3 trigonometric ratios.
Sin θ = ----------------
Cos θ = ----------------
Tan θ = ---------------
Csc θ = ----------------
Sec θ = ----------------
Cot θ = ---------------
2) What MODE should your calculator be in: __________________. How do you check?
3) Use your calculator to find the following values. Round to the nearest hundredth.
sin 25° =_______
tan 17° = _______
cos 48° = _______
4) Use your calculator to find the following values. Round to the nearest degree.
________ cos α =
3
4
_______ sin β =
2
11
________ tan θ =
9
7
Use the given triangle to determine the following ratios.
5. sin α =
α
6. cot α =
15
9
7. tan α =
8. csc α =
β
12
9. cos α =
10. sec α =
For each problem, set up the equation and solve for the variable. Round to the nearest hundredth for sides,
and nearest degree for angles.
11.
12.
13.
a
41°
b
8
27
59°
27°
15
b
b
Set up equation:
Set up equation:
Set up equation:
Solution: b = _________
Solution: b = _________
Solution: a = _________
Name: ______________________ Date: ________
14.
34
15.
18
α
16.
12
7
18
β
β
9
Set up equation:
Set up equation:
Set up equation:
Solution: α = _________
Solution: β = _________
Solution: β = _________
For each problem, draw a picture, set up equation and solve. (4 points each)
17. A plane is 575 ft directly above Paula’s house. The pilot can see the airport at a 35° of depression. How far
away is Paula’s house from the airport?
Picture:
Equation:
Solution:
18. A 16 foot ladder is leaning against a house. If the ladder reaches 10 feet up the house, what angle is formed
by the ladder and the house?
Picture:
Equation:
Solution:
19. A 35 foot vertical pole creates a shadow of 56 feet. What is the elevation of the sun with the ground?
Picture:
Equation:
Solution:
* PRE AP 20. A plane takes off at an elevation of 20°. In its path is the tower of 170 feet. If the plane at takeoff
is 500 feet away from the tower, will it clear the tower? If yes, by how much?
Picture:
Equation/Solution:
Answer:
* PRE AP 21. At a point 225 ft from the base of a cliff, the angle of elevation to the first ridge is 34° and to the
top of the cliff the angle of elevation is 71°. How much higher is the top of the cliff as compared to the first
ridge?
Picture:
Equation/Solution:
Answer:
Name: ______________________ Date: ________
22. Fill in the complete unit circle
PRE AP – Use trig ratios and the unit circle to find the indicated variable.
π 
 −3π 
23. cos 450
24. cot  
25. sec 

6
 4 
26. sin(−450 )
29. cos ( −1350 ) = x
32. If sin ( x ) =
7
−π
6
27. cot ( −1200 ) = 4x
28. cos
30. sin 2100 = x − 6
31. sec ( −300 )
3
, what are the ratios of csc ( x ) and cot ( x ) ?
5