TRIGNOMETRY

Introduction to Trigonometry

Trigonometry (from Greek trigonon "triangle" + metron "measure") 

Trigonometry ... is all about triangles.

Right Angled Triangle

A right-angled triangle (the right angle is shown by the little box in the corner) has names for each side: Adjacent is adjacent to the angle "θ", Opposite is opposite the angle, and the longest side is the Hypotenuse.

Angles

Angles (such as the angle "θ" above) can be in Degrees or Radians. Here are some examples:

Right Angle	90°	π/2
__ Straight Angle	180°	π
Full Rotation	360°	2π

"Sine, Cosine and Tangent"

The three most common functions in trigonometry are Sine, Cosine and Tangent. You will use them a lot!
They are simply one side of a triangle divided by another.
For any angle "θ":

Sine Function: sin(θ) = Opposite / Hypotenuse Cosine Function: cos(θ) = Adjacent / Hypotenuse Tangent Function: tan(θ) = Opposite / Adjacent

Example: What is the sine of 35°?

Using this triangle (lengths are only to one decimal place): sin(35°) = Opposite / Hypotenuse = 2.8/4.9 = 0.57...

Sine, Cosine and Tangent are often abbreivated to sin, cos and tan.

Basic formulas

sec(t) = 1/cos(t)

csc(t) = cosec(t) = 1/sin(t)

cos2(t) + sin2(t) = 1

1 + tan2(t) = sec2(t)

1 + cot2(t) = csc2(t)

Sum and Difference Formulas

Double Angle Formulas

Triple Angle Formulas

Half Angle Formula

Product to Sum Formulas

Sum to Product Formulas

TRIGONOMETRY RATIOS

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