Mr. Integral

THE BIG IDEA

Trigonometry

How does an angle become a number?

Start with a right triangle, then extend its ratios around a circle. The same picture explains signs, repeating values and why an inverse trig function needs a restricted range.

Begin the first lesson →See the lesson route ↓

8 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Triangle ratios
  2. extending around a circle gives02The unit circle
  3. shared geometry connects03Identities
  4. reversing a ratio requires04Inverse angles

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Basic Trigonometry4 lessons
  1. 01Ratios in a Right TriangleChoose a trigonometric ratio from the sides you know.
  2. 02Values at 30, 45 and 60 DegreesRecover exact trig values from special triangles.
  3. 03The Unit CircleRead sine and cosine from a point on the unit circle.
  4. 04The Identities Calculus AssumesUse an identity with the correct quadrant information.
Inverse Trigonometric Functions4 lessons
  1. 05Inverse Trig: Choosing One AngleExplain why an inverse trig function needs a restricted output interval.
  2. 06ArcsinSelect the principal angle returned by arcsine.
  3. 07ArccosUse the principal range of arccosine.
  4. 08Arctan and ArccotSeparate tangent inversion from reciprocal notation.