ACT Questions: Trigonometry

Videos, examples, solutions, activities and worksheets to help ACT students review some trigonometry questions.

What do you need to know about trigonometry in the ACT?

1. How to use SOHCAHTOA?
   
2. How to solve triangles?
   
3. How to use some Trigonometric Identities?
   
4. How to recognize the Trigonometric Graphs?

Basic Trig ACT prep - SOHCAHTOA
Examples:

1. For the triangle shown below, what is the value of sin z?
2. In the right triangle below, which of the following statements is true about ∠A?
3. In the right triangle below, if tan θ=2/√77, then sin θ =?
4. In triangle ACB shown below, sin A = 3/7 and the measure of CB is 14 inches. What is the measure of AB in inches?
5. If csc α = 4/3, and α is the measure of an acute angle, then cos α = ?
6. The radio station WEST is erecting a new transmitting tower that is 300 feet tall. A support wire will be attached to the ground at a 70° angle at point A and to the tower 260 feet up at point B, as shown below. The wire must be at least as long as AB. Which of the following expresses the length of AB, in feet?
7. Right triangle ABC has angle measures α, β, and γ degrees and side lengths a, b, and c inches, as illustrated below. Which of the following is true about the value of the product tan β tan γ?
8. The lengths, in feet, of the sides of right triangle ABC are as shown in the diagram below, with x > 0.
   What is the cotangent of angle A, in terms of x?
9. What is the measure of an angle in degrees if it measures 2π/3 radians?
10. What is the measure of an angle in radians if it measures 60°?
11. The measure of each interior angle of a regular polygon with n sides is ((n-2)180)/n degrees. What is the measure of each interior angle of a regular polygon with n sides, in radians?
12. For 0 < x < 2π, if sin x > 0 and cos x < 0, what are the possible values of x?
13. What is sin π/12 given that π/12 = π/3 - π/4 and that sin(α - β) = (sinα)(cosβ) - (cosα)(sinβ)
14. A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 2 vessels is 5°. The approximate distance, in miles, from the cargo ship to the fishing boat is given by which of the following expressions?

ACT Prep - Trigonometric Identities
Examples

1. Whenever sin x/tan x is defined, it is equivalent to:
   
2. Where defined, cos 3x sec 3x =
   
3. For 0 < x < 90°, tan x - tan(-x) + sin x - sin(-x) + cos x - cos(-x) =
   
4. For any acute angle with measure A, sin(90° - A) =
   
5. For 0 < x < π/2, the expression sin x/√(1 - sin²x) - √(1 - sin²x)/cos x is
   
6. tan²x + 1 =
   

ACT Math Test: Trigonometry Problems
Trig doesn’t have to be hard! Take a look at this ACT-Style Trig problem.
Example: a 10ft ladder leaning against a storage shed just reaches the top of the shed when it makes an angle of 70° with thr ground. Which of the following expression involving the sine function can be used to find h, the height of the shed?
A. sin(10 - 70°)
B. 10sin70°
C. 1/(10sin70°)
D. 10/sin70°
E. sin70°/10

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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