courses › Trigonometry

Radians, exact values, and signs in each quadrant.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 32.

Sign in to start

Builds on: Right-triangle trig (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Degrees to radians par 12 s not tried yet

  worked example

  120° is kπ radians. What is k? Give a fraction or a whole number.

  Answer: 2/3

  1. Multiply by π/180: 120/180 = 2/3, so 120° = 2π/3 radians.

• Radians to degrees par 8 s not tried yet

  worked example

  Convert π radians to degrees.

  Answer: 180

  1. π radians is 180°.

• Signs by quadrant par 11 s not tried yet

  worked example

  An angle θ has cos θ < 0 and sin θ > 0. Which quadrant is θ in?

  1. quadrant IV
  2. quadrant III
  3. quadrant II
  4. quadrant I

  Answer: quadrant II

  1. cos θ < 0 in quadrants II and III.
  2. sin θ > 0 in quadrants I and II.
  3. Both together: quadrant II.

• Exact values par 10 s not tried yet

  worked example

  What is the exact value of sin 315°?

  1. −√3/2
  2. −√2/2
  3. √2/2
  4. √3/2

  Answer: −√2/2

  1. 315° is 45° short of 360°, in quadrant IV, where sine is negative: sin 315° = −sin 45° = −√2/2.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

No rounds yet.