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Unit Circle Exact Values — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Give the exact value. Write "undefined" if the value is undefined.
How to solve
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Example
Find the exact value of cos(210°).
Answer: -√32
Not quite. The answer is
💡 270° is the point (0, -1) on the unit circle. Sine is the y-coordinate, so sin(270°) = -1.
✓ Correct!
Not quite. The answer is
💡 270° is the point (0, -1) on the unit circle. Sine is the y-coordinate, so sin(270°) = -1.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of tan(270°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 From the 30°-60°-90° triangle, cos(30°) = √32.
✓ Correct!
Not quite. The answer is
💡 From the 30°-60°-90° triangle, cos(30°) = √32.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of tan(0°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 135° is in quadrant II, so the reference angle is 180° − 135° = 45°. sin(45°) = √22, and sine is positive in quadrant II, so sin(135°) = √22.
✓ Correct!
Not quite. The answer is
💡 135° is in quadrant II, so the reference angle is 180° − 135° = 45°. sin(45°) = √22, and sine is positive in quadrant II, so sin(135°) = √22.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of cos(45°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 135° is in quadrant II, so the reference angle is 180° − 135° = 45°. tan(45°) = 1, and tangent is negative in quadrant II, so tan(135°) = -1.
✓ Correct!
Not quite. The answer is
💡 135° is in quadrant II, so the reference angle is 180° − 135° = 45°. tan(45°) = 1, and tangent is negative in quadrant II, so tan(135°) = -1.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of sin(225°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 From the 45°-45°-90° triangle, sin(45°) = √22.
✓ Correct!
Not quite. The answer is
💡 From the 45°-45°-90° triangle, sin(45°) = √22.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of tan(225°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 315° is in quadrant IV, so the reference angle is 360° − 315° = 45°. cos(45°) = √22, and cosine is positive in quadrant IV, so cos(315°) = √22.
✓ Correct!
Not quite. The answer is
💡 315° is in quadrant IV, so the reference angle is 360° − 315° = 45°. cos(45°) = √22, and cosine is positive in quadrant IV, so cos(315°) = √22.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of cos(120°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 0° is the point (1, 0) on the unit circle. Tangent is yx = 01 = 0, so tan(0°) = 0.
✓ Correct!
Not quite. The answer is
💡 0° is the point (1, 0) on the unit circle. Tangent is yx = 01 = 0, so tan(0°) = 0.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of sin(150°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 120° is in quadrant II, so the reference angle is 180° − 120° = 60°. tan(60°) = √3, and tangent is negative in quadrant II, so tan(120°) = -√3.
✓ Correct!
Not quite. The answer is
💡 120° is in quadrant II, so the reference angle is 180° − 120° = 60°. tan(60°) = √3, and tangent is negative in quadrant II, so tan(120°) = -√3.
💡 How to solve: Unit Circle Exact Values
Find the reference angle and the quadrant, then use the special values: sin 30° = 12, sin 45° = √22, sin 60° = √32 (cos is the reverse), and tan = sin ÷ cos. Make sin positive in quadrants I and II, cos positive in I and IV, and tan positive in I and III. Write "undefined" when cos = 0 for tan.
Try a similar one
Find the exact value of cos(300°).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Unit Circle Exact Values — Easy Worksheet 2
Give the exact value. Write "undefined" if the value is undefined.