Trigonometry

Aug 12, 2023 permanent

This is my Topic Overview (Zettlekasten) for Trigonometry.

Trigonometry is the study of angles and distances.

Triangles

A shape with 3 sides.

The angles of a triangle are a measure of the distance between each side.

In every triangle, the sum of all 3 angles adds to 180°.

One type of triangle that usually makes sense to understand first is the [[right-angle triangle]]. This is where one angle is 90°.

In a right triangle, we can examine the 2 other angles. We name the sides of the triangle specials names that help us:

  • Opposite: the side directly opposite the angle.
  • Adjacent: the side opposite the angle.
  • Hypotenuse: the longest side of the triangle.

The ratios between the sides of a right-angle triangle have do a bunch of really useful things and are named as follows:

  • Sine
    • The ratio between opposite and hypotenuse.
  • Cosine
    • The ratio between adjacent and hypotenuse.
  • Tangent
    • The ratio between opposite and adjacent.

If we set the size of the hypotenuse to be 1, notice that sine is simply the size of the opposite angle. And cosine is simply the size of the adjacent angle.

These functions also have an inverse Inverse Trigonomentric Functions.

The functions have some useful Trig Angle Identities that can help solve trig problems algebraically.