trigonometry test with answers pdf

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31-01-2025

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I cannot create a PDF file. I am a text-based AI and do not have the capability to generate or manipulate files. However, I can provide you with a trigonometry test with answers in a text format. Remember that this is for practice and shouldn't be used for cheating on an actual assessment.

Trigonometry Test with Answers

This test covers basic trigonometric functions, identities, and applications. Remember to show your work for full credit!

Section 1: Basic Trigonometric Functions

1. Find the values of sin θ, cos θ, and tan θ for the angle θ in a right-angled triangle with opposite side = 3, adjacent side = 4, and hypotenuse = 5.

   • Answer: sin θ = 3/5, cos θ = 4/5, tan θ = 3/4

2. If sin θ = 1/2, find cos θ and tan θ (assuming θ is in the first quadrant).

   • Answer: cos θ = √3/2, tan θ = 1/√3 or √3/3

3. What is the value of sin 30°?

   • Answer: 1/2

4. What is the value of cos 60°?

   • Answer: 1/2

5. What is the value of tan 45°?

   • Answer: 1

Section 2: Trigonometric Identities

1. Simplify the expression: sin²θ + cos²θ

   • Answer: 1

2. Use trigonometric identities to simplify: (1 + tan²θ)

   • Answer: sec²θ

3. Verify the identity: tan θ = sin θ / cos θ

   • Answer: This identity is fundamental and requires only the definitions of tan, sin, and cos to verify. A proof could involve writing out these definitions and showing the equivalence.

Section 3: Applications of Trigonometry

1. A ladder leans against a wall. The ladder is 10 meters long, and the base of the ladder is 6 meters from the wall. What angle does the ladder make with the ground?

   • Answer: Use cos θ = adjacent/hypotenuse. cos θ = 6/10 = 0.6. Therefore, θ = arccos(0.6) ≈ 53.13°

2. A surveyor measures the angle of elevation to the top of a building as 30°. If the surveyor is 50 meters from the base of the building, how tall is the building?

   • Answer: Use tan θ = opposite/adjacent. tan 30° = height/50. Height = 50 * tan 30° ≈ 28.87 meters

Remember: This is a simplified test and covers only basic concepts. A more comprehensive trigonometry test would include more advanced topics like inverse trigonometric functions, trigonometric equations, and graphs of trigonometric functions. You should consult your textbook or other learning resources for more complete coverage.