Reference Angles & Basic Graphs of Sine & Cosine

A reference angle is the acute angle formed by the terminal ray of an angle and the x-axis. The trigonometric functions of an angle are the same as the trigonometric functions of its reference angle except for the positive or negative sign.

Examples:

Angle Reference Angle

50^o 50^o
135^o 45^o (180^o - 135^o)
210^o 30^o (210^o - 180^o)
330^o 30^o (360^o - 330^o)
510^o 30^o (Coterminal to 150^o; 180^o - 150^o = 30^o)

Special Angles

Angle	*0^o* *= 0*	*30^o* *= p* 6	*45^o* *= p* 4	*60^o* *= p* 3	*90^o* *= p* 2
*Sin 0*	*\/0 = 0* 2	*\/1 = 1* *2 2*	*\/2* 2	*\/3* 2	*\/4 = 1* 2
*Cos 0*	*\/4 = 1* 2	*\/3* 2	*\/2* 2	*\/1 = 1* *2 2*	*\/0 = 0* 2

Graphs

y = sin x for 0 < x < 2p
Domain: all real numbers
Range: -1 < y < 1
Period: 2p

y = cos x for 0 < x < 2p
Domain: all real numbers
Range: -1 < y < 1
Period: 2p

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