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Grade 12 Trig Identities & Equations Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 1: TrigonometryIdentities & EquationsCCSS F-TF.C.8

Using the Pythagorean identity and solving basic trig equations on 0° to 360°. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Trig Identities & Equations

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Identities & Equations · CCSS F-TF.C.8

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

If sin θ = 5/13 and θ is in Quadrant I, find cos θ.

Answer: 12/13

RememberUnit circle and trig laws

(1, 0)30° (√3/2, ½)45° (√2/2, √2/2)60° (½, √3/2)(0, 1)(−1, 0)(0, −1)Point on the circle = (cos θ, sin θ)tan θ = sin θ ÷ cos θ180° = π radianssin² θ + cos² θ = 1Law of sines: a/sin A = b/sin BLaw of cosines: c² = a² + b² − 2ab cos C
  1. 1

    Solve for 0° ≤ x < 360°: sin x = 0

    Answer
  2. 2

    If sin θ = 7/25 and θ is in Quadrant I, find cos θ.

    Answer
  3. 3

    Simplify: 1 - sin²θ

    Answer
  4. 4

    Simplify: sin θ / cos θ

    Answer
  5. 5

    If sin θ = 3/5 and θ is in Quadrant I, find cos θ.

    Answer
  6. 6

    Solve for 0° ≤ x < 360°: tan x = -√3

    Answer
  7. 7

    Simplify: sin²θ + cos²θ

    Answer
  8. 8

    Simplify: 1 - cos²θ

    Answer
  9. 9

    Solve for 0° ≤ x < 360°: cos x = 1

    Answer
  10. 10

    If sin θ = 8/17 and θ is in Quadrant I, find cos θ.

    Answer
  11. 11

    Solve for 0° ≤ x < 360°: cos x = √3/2

    Answer
  12. 12

    Solve for 0° ≤ x < 360°: sin x = 1/2

    Answer

★ Challenge corner for fast finishers

On a grid, you walk from the bottom-left corner to a point 3 blocks right and 3 blocks up, moving only right or up. How many different shortest paths are there?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/trig_equations

Answer key (click to show)
  1. 1.0°, 180°
  2. 2.24/25
  3. 3.cos²θ
  4. 4.tan θ
  5. 5.4/5
  6. 6.120°, 300°
  7. 7.1
  8. 8.sin²θ
  9. 9.0°
  10. 10.15/17
  11. 11.30°, 330°
  12. 12.30°, 150°
  13. ★20 (challenge corner)

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