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Functions and Trigonometry Worksheet Generator

Unit circle, right triangle trig, laws of sines and cosines, transformations, exponentials, logarithms, and inverse functions. No AI, no credits.

Grade 9 – Grade 12No account needed

Functions and trigonometry activities: unit circle exact values, right triangle trigonometry, laws of sines and cosines (the ambiguous SSA case is published only when the number of solutions is known and shown in the key), transformations and graphs, exponentials and logarithms, and inverse functions with domain and range. States radians or degrees. Every answer is computed by code and verified by a second independent method. No AI, so it never uses a generation credit.

What students practice

  • Functions
  • Trigonometry
  • Algebra

Live sample sheet

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Functions and Trigonometry

1. Find sin(3π/2). (Exact value)
270°
2. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
3. Find cos(π). (Exact value)
180°
4. In a right triangle with legs 3 and 4 and hypotenuse 5, find tan(θ) where θ is opposite to side 3.
b=4a=3c=5
5. Find tan(3π/2). (Exact value)
270°
6. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
7. Find tan(5π/6). (Exact value)
150°
8. In a right triangle with legs 8 and 15 and hypotenuse 17, find sin(θ) where θ is opposite to side 8.
b=15a=8c=17
9. Find sin(π/2). (Exact value)
90°
10. In a right triangle with legs 8 and 15 and hypotenuse 17, find tan(θ) where θ is opposite to side 8.
b=15a=8c=17

Answer Key — Functions and Trigonometry

1. Find sin(3π/2). (Exact value)
270°
sin(3π/2) = -1
Numerical check: sin(270°) ≈ -1.0000
Answer: -1
2. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
tan = opposite / adjacent = 6 / 8
Answer: 6/8
3. Find cos(π). (Exact value)
180°
cos(π) = -1
Numerical check: cos(180°) ≈ -1.0000
Answer: -1
4. In a right triangle with legs 3 and 4 and hypotenuse 5, find tan(θ) where θ is opposite to side 3.
b=4a=3c=5
tan = opposite / adjacent = 3 / 4
Answer: 3/4
5. Find tan(3π/2). (Exact value)
270°
tan(3π/2) = undefined
Numerical check: tan(270°) ≈ 5443746451065123.0000
Answer: undefined
6. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
tan = opposite / adjacent = 6 / 8
Answer: 6/8
7. Find tan(5π/6). (Exact value)
150°
tan(5π/6) = -√3/3
Numerical check: tan(150°) ≈ -0.5774
Answer: -√3/3
8. In a right triangle with legs 8 and 15 and hypotenuse 17, find sin(θ) where θ is opposite to side 8.
b=15a=8c=17
sin = opposite / hypotenuse = 8 / 17
Answer: 8/17
9. Find sin(π/2). (Exact value)
90°
sin(π/2) = 1
Numerical check: sin(90°) ≈ 1.0000
Answer: 1
10. In a right triangle with legs 8 and 15 and hypotenuse 17, find tan(θ) where θ is opposite to side 8.
b=15a=8c=17
tan = opposite / adjacent = 8 / 15
Answer: 8/15

Assumptions and Conventions

Assumptions:
  • All angles are in radians unless stated otherwise.
  • The unit circle has radius 1.
  • Right triangles use SOH CAH TOA.
Conventions:
  • Exact values use fractions and radicals.
  • Decimal answers round to 2 places.
  • Law of sines: a/sin(A) = b/sin(B) = c/sin(C).
  • Law of cosines: c² = a² + b² - 2ab·cos(C).

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Frequently asked questions

Do students need an account to use the Functions and Trigonometry?

No. Students never need an account. They open a shared link or join with a code.

Can I print the Functions and Trigonometry without signing up?

Yes. This tool computes answers by code, so you can generate, preview and print worksheet without an account. A free account adds saving and student links.

How are the answers computed?

Every answer is computed by code and verified by a second independent method. No AI is used.

What grades is the Functions and Trigonometry for?

This tool fits Grade 9 – Grade 12.

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Functions and Trigonometry

1. Find sin(3π/2). (Exact value)
270°
2. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
3. Find cos(π). (Exact value)
180°
4. In a right triangle with legs 3 and 4 and hypotenuse 5, find tan(θ) where θ is opposite to side 3.
b=4a=3c=5
5. Find tan(3π/2). (Exact value)
270°
6. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
7. Find tan(5π/6). (Exact value)
150°
8. In a right triangle with legs 8 and 15 and hypotenuse 17, find sin(θ) where θ is opposite to side 8.
b=15a=8c=17
9. Find sin(π/2). (Exact value)
90°
10. In a right triangle with legs 8 and 15 and hypotenuse 17, find tan(θ) where θ is opposite to side 8.
b=15a=8c=17

Answer Key — Functions and Trigonometry

1. Find sin(3π/2). (Exact value)
270°
sin(3π/2) = -1
Numerical check: sin(270°) ≈ -1.0000
Answer: -1
2. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
tan = opposite / adjacent = 6 / 8
Answer: 6/8
3. Find cos(π). (Exact value)
180°
cos(π) = -1
Numerical check: cos(180°) ≈ -1.0000
Answer: -1
4. In a right triangle with legs 3 and 4 and hypotenuse 5, find tan(θ) where θ is opposite to side 3.
b=4a=3c=5
tan = opposite / adjacent = 3 / 4
Answer: 3/4
5. Find tan(3π/2). (Exact value)
270°
tan(3π/2) = undefined
Numerical check: tan(270°) ≈ 5443746451065123.0000
Answer: undefined
6. In a right triangle with legs 6 and 8 and hypotenuse 10, find tan(θ) where θ is opposite to side 6.
b=8a=6c=10
tan = opposite / adjacent = 6 / 8
Answer: 6/8
7. Find tan(5π/6). (Exact value)
150°
tan(5π/6) = -√3/3
Numerical check: tan(150°) ≈ -0.5774
Answer: -√3/3
8. In a right triangle with legs 8 and 15 and hypotenuse 17, find sin(θ) where θ is opposite to side 8.
b=15a=8c=17
sin = opposite / hypotenuse = 8 / 17
Answer: 8/17
9. Find sin(π/2). (Exact value)
90°
sin(π/2) = 1
Numerical check: sin(90°) ≈ 1.0000
Answer: 1
10. In a right triangle with legs 8 and 15 and hypotenuse 17, find tan(θ) where θ is opposite to side 8.
b=15a=8c=17
tan = opposite / adjacent = 8 / 15
Answer: 8/15

Assumptions and Conventions

Assumptions:
  • All angles are in radians unless stated otherwise.
  • The unit circle has radius 1.
  • Right triangles use SOH CAH TOA.
Conventions:
  • Exact values use fractions and radicals.
  • Decimal answers round to 2 places.
  • Law of sines: a/sin(A) = b/sin(B) = c/sin(C).
  • Law of cosines: c² = a² + b² - 2ab·cos(C).
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