courses › Trigonometry

Use trig identities and solve trig equations.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 43.

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Builds on: Radians & the unit circle (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.

• sin² + cos² = 1 par 20 s not tried yet

  worked example

  sin θ = −20/29 and θ is in quadrant IV. What is cos θ? Give a fraction.

  Answer: 21/29

  1. cos² θ = 1 − sin² θ = 1 − 400/841 = 441/841, so cos θ = ±21/29.
  2. Cosine is positive in quadrant IV, so cos θ = 21/29.

• Period par 15 s not tried yet

  worked example

  The period of y = sin(2x) is kπ. What is k? Give a fraction or a whole number.

  Answer: 1

  1. The period of sin(bx) is 2π ÷ b = 2π ÷ 2 = π, so k = 1.

• Double angle par 25 s not tried yet

  worked example

  sin θ = −9/41 and cos θ = −40/41. What is cos 2θ? Give a fraction.

  Answer: 1519/1681

  1. cos 2θ = cos² θ − sin² θ = 1600/1681 − 81/1681 = 1519/1681.

• Solve a trig equation par 25 s not tried yet

  worked example

  Solve sin x = 1/2 for 0° ≤ x < 360°. Enter both answers in degrees, smaller first.

  Answer: (30, 150)

  1. The reference angle is 30°, because sin 30° = 1/2.
  2. Sine is positive in quadrants I and II: 30° and 180° − 30° = 150°.

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.