QuickNotes™

Main definitions and formulas:

A 45-45-90 triangle has side lengths in proportion to 1-1-√ 2.
A 30-60-90 triangle has side lengths in proportion to 1-√ 3-2.
Degrees
Radians
Cosine
Sine

0
0
1
0

30
π
6

√ 3
2

1
2

45
π
4

√ 2
2

√ 2
2

60
π
3

1
2

√ 3
2

90
π
2

0
1
Use these values to find sines and cosines in other quadrants. The mnemonic ASTC (All Students Take Calculus) helps you remember which ones are positive in which quadrant. (All, Sine, Tangent, Cosine)

Example 1:

Convert 120^° to radians, identify its quadrant, and find its cosine and sine.

Example 2:

Convert (5π/3)^R to degrees, identify its quadrant, and find its cosine and sine.

Example 3:

Identify all angles between 0 and 2π whose sine is − [1/2], in both degrees and radians, and identify which quadrant each is in.

Example 4:

Convert 225^° to radians, identify its quadrant, and find its cosine and sine.

Example 5:

Identify all angles between 0 and 2π whose cosine is − (√3/2), in both degrees and radians, and identify which quadrant each is in.

Discussion

I. Trigonometric Functions
	Angles	39:05
	Sine and Cosine Functions	43:16
	Sine and Cosine Values of Special Angles	33:05
	Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D	52:03
	Tangent and Cotangent Functions	36:04
	Secant and Cosecant Functions	27:18
	Inverse Trigonometric Functions	32:58
	Computations of Inverse Trigonometric Functions	31:08
II. Trigonometric Identities
	Pythagorean Identity	19:11
	Identity Tan(squared)x+1=Sec(squared)x	23:16
	Addition and Subtraction Formulas	52:52
	Double Angle Formulas	29:05
	Half-Angle Formulas	43:55
III. Applications of Trigonometry
	Trigonometry in Right Angles	25:43
	Law of Sines	56:40
	Law of Cosines	49:05
	Finding the Area of a Triangle	27:37
	Word Problems and Applications of Trigonometry	34:25
	Vectors	46:42
IV. Complex Numbers and Polar Coordinates
	Polar Coordinates	67:35
	Complex Numbers	35:59
	Polar Form of Complex Numbers	40:43
	DeMoivre's Theorem	57:37