Trigonometry

Trig ratios, right-triangle trigonometry, the sine and cosine laws, the unit circle and the identities.

8 sheets · 64 questions · one answer key · 10 pages

Recommended for grades 9–11

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Trig ratios Sheet 1 of 8

Write a trigonometric ratioWrite sine, cosine and tangent ratios

Name: Date:

Write each ratio as a fraction. Read the sides straight off the triangle.

1 cos B =

2 sin B =

3 cos A =

4 tan B =

5 tan B =

6 cos A =

7 sin B =

8 tan A =

Right-triangle trigonometryFind a side with trigonometry

Name: Date:

Find the side marked x, to one decimal place. Use a calculator.

1 cm

2 cm

3 cm

4 cm

5 cm

6 cm

7 cm

8 cm

Right-triangle trigonometryFind an angle with trigonometry

Name: Date:

Find the angle marked x, to the nearest degree. Use a calculator.

1 degrees

2 degrees

3 degrees

4 degrees

5 degrees

6 degrees

7 degrees

8 degrees

Laws of sines and cosinesUse the law of sines

Name: Date:

Use the law of sines. Round each length to one decimal place.

1In △ABC, a = 11, ∠A = 30°, ∠B = 75°. Find b:

2In △ABC, a = 12, ∠A = 40°, ∠B = 50°. Find b:

3In △ABC, a = 10, ∠A = 50°, ∠B = 70°. Find b:

4In △ABC, a = 9, ∠A = 45°, ∠B = 55°. Find b:

5In △ABC, a = 5, ∠A = 55°, ∠B = 65°. Find b:

6In △ABC, a = 7, ∠A = 50°, ∠B = 60°. Find b:

7In △ABC, a = 7, ∠A = 40°, ∠B = 60°. Find b:

8In △ABC, a = 8, ∠A = 35°, ∠B = 80°. Find b:

Laws of sines and cosinesUse the law of cosines

Name: Date:

Use the law of cosines. Round each length to one decimal place.

1In △ABC, a = 6, b = 11, ∠C = 35°. Find c:

2In △ABC, a = 8, b = 12, ∠C = 50°. Find c:

3In △ABC, a = 10, b = 6, ∠C = 45°. Find c:

4In △ABC, a = 5, b = 8, ∠C = 60°. Find c:

5In △ABC, a = 9, b = 9, ∠C = 70°. Find c:

6In △ABC, a = 5, b = 7, ∠C = 80°. Find c:

7In △ABC, a = 12, b = 7, ∠C = 55°. Find c:

8In △ABC, a = 6, b = 9, ∠C = 65°. Find c:

Unit circleConvert between degrees and radians

Name: Date:

Convert between degrees and radians. Leave radians in terms of π.

160° in radians =

230° in radians =

3300° in radians =

4210° in radians =

55π4 in degrees =

63π4 in degrees =

7225° in radians =

8π2 in degrees =

Unit circleRead exact values off the unit circle

Name: Date:

Give each exact value. Leave surds and fractions exact — no calculator.

1sin 90° =

2cos 60° =

3tan 0° =

4cos 30° =

5tan 60° =

6sin 60° =

7sin 45° =

8cos 90° =

Trigonometric identitiesUse the Pythagorean identity

Name: Date:

Use sin²A + cos²A = 1. Each answer is a fraction in lowest terms.

1If sin A = 35, cos A =

2If cos A = 1517, sin A =

3If sin A = 725, cos A =

4If sin A = 817, cos A =

5If sin A = 2029, cos A =

6If cos A = 2129, sin A =

7If sin A = 941, cos A =

8If cos A = 45, sin A =

Power Pack · TrigonometryAnswer key

Trig ratios

1. cos B (legs 4, 3, hyp 5) = 3/52. sin B (legs 35, 12, hyp 37) = 35/373. cos A (legs 8, 15, hyp 17) = 15/174. tan B (legs 4, 3, hyp 5) = 4/35. tan B (legs 21, 20, hyp 29) = 21/206. cos A (legs 3, 4, hyp 5) = 4/57. sin B (legs 21, 20, hyp 29) = 21/298. tan A (legs 9, 40, hyp 41) = 9/40

Finding a side

1. 25°, adj 8 → opp x = 3.72. 30°, opp 19 → hyp x = 383. 25°, adj 15 → opp x = 74. 35°, opp 14 → adj x = 205. 25°, hyp 10 → adj x = 9.16. 60°, adj 6 → hyp x = 127. 30°, opp 12 → hyp x = 248. 30°, adj 7 → opp x = 4

Finding an angle

1. opp 16, adj 15 → x = 47°2. opp 14, adj 16 → x = 41°3. opp 13, adj 12 → x = 47°4. opp 11, adj 16 → x = 35°5. opp 15, adj 12 → x = 51°6. opp 9, adj 7 → x = 52°7. opp 14, adj 15 → x = 43°8. opp 10, adj 3 → x = 73°

The sine rule

1. In △ABC, a = 11, ∠A = 30°, ∠B = 75°. Find b: 21.32. In △ABC, a = 12, ∠A = 40°, ∠B = 50°. Find b: 14.33. In △ABC, a = 10, ∠A = 50°, ∠B = 70°. Find b: 12.34. In △ABC, a = 9, ∠A = 45°, ∠B = 55°. Find b: 10.45. In △ABC, a = 5, ∠A = 55°, ∠B = 65°. Find b: 5.56. In △ABC, a = 7, ∠A = 50°, ∠B = 60°. Find b: 7.97. In △ABC, a = 7, ∠A = 40°, ∠B = 60°. Find b: 9.48. In △ABC, a = 8, ∠A = 35°, ∠B = 80°. Find b: 13.7

The cosine rule

1. In △ABC, a = 6, b = 11, ∠C = 35°. Find c: 7.02. In △ABC, a = 8, b = 12, ∠C = 50°. Find c: 9.23. In △ABC, a = 10, b = 6, ∠C = 45°. Find c: 7.24. In △ABC, a = 5, b = 8, ∠C = 60°. Find c: 7.05. In △ABC, a = 9, b = 9, ∠C = 70°. Find c: 10.36. In △ABC, a = 5, b = 7, ∠C = 80°. Find c: 7.97. In △ABC, a = 12, b = 7, ∠C = 55°. Find c: 9.88. In △ABC, a = 6, b = 9, ∠C = 65°. Find c: 8.4

Degrees and radians

1. 60° in radians = π/32. 30° in radians = π/63. 300° in radians = 5π/34. 210° in radians = 7π/6

Power Pack · TrigonometryAnswer key

Degrees and radians

5. 5π/4 in degrees = 225°6. 3π/4 in degrees = 135°7. 225° in radians = 5π/48. π/2 in degrees = 90°

Values on the unit circle

1. sin 90° = 12. cos 60° = 1/23. tan 0° = 04. cos 30° = √3/25. tan 60° = √36. sin 60° = √3/27. sin 45° = √2/28. cos 90° = 0

Trig identities

1. If sin A = 3/5, cos A = 4/52. If cos A = 15/17, sin A = 8/173. If sin A = 7/25, cos A = 24/254. If sin A = 8/17, cos A = 15/175. If sin A = 20/29, cos A = 21/296. If cos A = 21/29, sin A = 20/297. If sin A = 9/41, cos A = 40/418. If cos A = 4/5, sin A = 3/5

Trigonometry

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