ACT math SOHCAHTOA and unit circle tips and practice
Master SOHCAHTOA and unit circle concepts for the ACT with practical examples and quick questions to boost your trigonometry skills.
Quiz(48 questions)
1. What does SOH stand for in trigonometry?
Terms in this Study Set(48)
SOHCAHTOA Basics(16)
SOHCAHTOA - What does SOH mean?
SOH stands for Sine = Opposite / Hypotenuse.
Find sin(30°).
sin(30°) = 1/2. Use SOH: Opposite (1) over Hypotenuse (2).
What does CAH represent?
CAH means Cosine = Adjacent / Hypotenuse.
True or False: Cos(90°) = 0. Why?
True. At 90°, the adjacent side is 0.
Tangent is represented by which ratio?
Tangent = Opposite / Adjacent.
True or False: tan(45°) = 1. Why?
True. Opposite and adjacent are equal.
Fill in the blank: sin(θ) = _____ / Hypotenuse.
Opposite.
Find cos(60°).
cos(60°) = 1/2. Adjacent (1) over Hypotenuse (2).
SOHCAHTOA - What does TOA mean?
TOA means Tangent = Opposite / Adjacent.
What is the sine of 0°?
sin(0°) = 0. No opposite side.
How to remember SOHCAHTOA?
Mnemonic: SOHCAHTOA or songs work well.
Calculate tan(30°).
tan(30°) = 1/√3 or approximately 0.577.
Convert degrees to radians: 180°.
180° = π radians.
What is the cosine of 0°?
cos(0°) = 1. Full adjacent side.
Fill in the blank: tan(θ) = _____ / Adjacent.
Opposite.
Find sin(90°).
sin(90°) = 1. Full height in the unit circle.
Unit Circle Applications(16)
What angle corresponds to 90 degrees on the unit circle?
The angle of 90 degrees corresponds to the point (0, 1) on the unit circle.
True or False: The coordinates for 180 degrees are (0, -1).
False. The coordinates for 180 degrees are (-1, 0).
Fill in the blank: The sine of 30 degrees is ___.
The sine of 30 degrees is 0.5.
What is the cosine value for 360 degrees?
The cosine value for 360 degrees is 1.
Compare sine and cosine for 45 degrees.
Both sine and cosine for 45 degrees are equal: sin(45°) = cos(45°) = .
What is the sine of 210 degrees?
The sine of 210 degrees is -0.5.
What coordinates represent 120 degrees on the unit circle?
The coordinates for 120 degrees are \\left(-\\frac{1}{2}, \\frac{\sqrt{3}}{2}\right).
True or False: The tangent of 90 degrees is defined.
False. The tangent of 90 degrees is undefined because it involves division by zero.
What is the reference angle for 150 degrees?
The reference angle for 150 degrees is 30 degrees.
Fill in the blank: The cosine of 270 degrees is ___.
The cosine of 270 degrees is 0.
What angle has coordinates (1, 0) on the unit circle?
The angle with coordinates (1, 0) is 0 degrees (or 360 degrees).
What is the sine value for 240 degrees?
The sine value for 240 degrees is -.
True or False: The coordinates for 315 degrees are (\\frac{\sqrt{2}}{2}, -\\frac{\sqrt{2}}{2}).
True. That's correct for 315 degrees.
What is the cosine of 135 degrees?
The cosine of 135 degrees is -.
What coordinates represent 330 degrees on the unit circle?
The coordinates for 330 degrees are \\left(\\frac{\sqrt{3}}{2}, -\\frac{1}{2}\right).
Calculate the tangent of 60 degrees.
The tangent of 60 degrees is .
Real-World Trigonometry Problems(16)
A ladder leans against a wall. Angle is 60°.
If the ladder is 10 feet long, how high does it reach? Use sine: Height = 10 * sin(60°) ≈ 8.66 feet.
True or False: Cosine relates to opposite over adjacent.
False. Cosine relates to adjacent over hypotenuse.
You walk 50 miles at 30° from north. What is the eastward distance?
Use cosine: Eastward distance = 50 * cos(30°) ≈ 43.30 miles.
Complete the sentence: In a right triangle, ____ = opposite/hypotenuse.
Sine
A tree casts a shadow 15 feet long. Angle of elevation is 45°.
Height of the tree = 15 * tan(45°) = 15 feet.
You throw a rock at a 40° angle. What is the vertical distance?
If distance is 20 feet: Height = 20 * sin(40°) ≈ 12.86 feet.
True or False: A 30° angle has a sine value of 0.5.
True. sin(30°) = 0.5.
A kite is flying at a height of 50 feet at a 60° angle.
How far away is it from you horizontally? Distance = 50 * tan(60°) ≈ 28.87 feet.
Fill in the blank: The cosine of 90° is ____.
0
You rent an apartment. Angle of elevation to a window is 30°.
If you're 20 feet away, height = 20 * tan(30°) ≈ 11.55 feet.
In a right triangle, if adjacent = 5 and hypotenuse = 13, find cosine.
Cosine = adjacent/hypotenuse = 5/13 ≈ 0.3846.
True or False: Tangent is opposite over adjacent.
True. tan(θ) = opposite/adjacent.
A ramp is 12 feet long. The angle with the ground is 30°.
What is the height of the ramp? Height = 12 * sin(30°) = 6 feet.
You drive 100 miles at a 45° angle northeast. Find northward distance.
Northward distance = 100 * sin(45°) ≈ 70.71 miles.
True or False: The sine of 60° is greater than the sine of 30°.
True. sin(60°) ≈ 0.866, sin(30°) = 0.5.
A boat sails 30 miles at a 70° angle from shore.
What is its eastward position? Eastward distance = 30 * cos(70°) ≈ 10.36 miles.
Questions in this Study Set(48)
1. What does SOH stand for in trigonometry?
2. What coordinates represent 270 degrees on the unit circle?
3. A baseball player hits a ball at a 45° angle. If the ball travels 100 feet, how high does it go?
4. If the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?
5. True or False: The sine of 90 degrees is 1.
6. True or False: The cosine function is defined as opposite over hypotenuse.
7. What does CAH mean in the context of trigonometry?
8. What is the reference angle for 300 degrees?
9. You are standing 30 feet away from a tree. The angle of elevation to the top of the tree is 60°. What is the height of the tree?
10. At 90°, what is the value of cos(90°)?
11. Fill in the blank: The cosine of 120 degrees is ___.
12. Fill in the blank: Sin(30°) equals _____.
13. Which of the following represents the tangent ratio?
14. What is the sine value for 45 degrees?
15. A ramp is 9 feet long and at a 30° angle to the ground. How high is the ramp?
16. If the opposite side and adjacent side are equal, what is tan(45°)?
17. Which of the following angles has coordinates (sqrt(3)/2, -1/2)?
18. You walk 40 miles at an angle of 30° from west. What is your northward distance?
19. Complete the statement: sin(θ) = _____ / Hypotenuse.
20. What is the cosine value for 180 degrees?
21. In a right triangle, if opposite = 6 and hypotenuse = 10, what is the sine of the angle?
22. What is cos(60°)?
23. True or False: The tangent of 45 degrees is 1.
24. True or False: The tangent of 45° is 1.
25. What does TOA stand for?
26. What angle corresponds to the point (-1, 0) on the unit circle?
27. A kite is flying at a height of 40 feet at a 30° angle from the ground. How far away is it from you horizontally?
28. What is the sine of 0°?
29. Fill in the blank: The sine of 240 degrees is ___.
30. You drive 80 miles at an angle of 60° from north. What is your eastward distance?
31. How can you remember SOHCAHTOA?
32. What is the cosine of 330 degrees?
33. Complete the sentence: In a right triangle, ____ = adjacent/hypotenuse.
34. Calculate tan(30°).
35. Which of the following is NOT a coordinate for an angle on the unit circle?
36. True or False: The sine of an angle can never be greater than 1.
37. Convert 180° to radians.
38. What is the tangent of 30 degrees?
39. A ladder leaning against a wall makes a 30° angle with the ground. If the ladder is 15 feet long, how high does it reach?
40. What is cos(0°)?
41. What is the sine value for 150 degrees?
42. You throw a ball at a 50° angle for a distance of 25 feet. What is the vertical distance it reaches?
43. Complete the statement: tan(θ) = _____ / Adjacent.
44. What is the sine of 360 degrees?
45. A boat sails 40 miles at a 60° angle from the shore. What is its northward position?
46. What is the value of sin(90°)?
47. Which angle corresponds to the coordinates (\\frac{1}{2}, \\frac{ oot{3}}{2}) on the unit circle?
48. What is NOT true about cosine?
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