Trigonometry

1^st Quadrant Measures of common angles:

    

Also, be able to draw accurate graphs of the sine and cosine functions

Conversions from other quadrants to 1^st quadrant:

Q2 to Q1:  p - q;        Q3 to Q1:  q - p;        Q4 to Q1:  2p - q.  (q in radians)

If you forget these, draw a circle and use symmetry and common sense.

Signs in other quadrants:

A mnemonic:  "All Students Take Calculus".  A = all are + in Q1; S = sine is + in Q2; T = tangent is + in Q3; C = cosine is + in Q4.

Inverse trig functions: 

y = sin^-1 x:    y will be in Q1 or Q4, use symmetry to get other answers.

y = cos^-1 x:   y will be in Q1 or Q2, use symmetry to get other answers.

y = tan^-1 x:   y will be in Q1 or Q4, use symmetry to get other answers.

   Fundamental Identities

cos² q  + sin² q  = 1

1 + tan² q  = sec² q

1 + cot² q  = csc² q

             sin q  = − sin(−q)                                          cosc q  = − csc(−q)

cos q  = cos(−q)                                             sec q  = sec(−q)

            tan q  = − tan(−q)                                         cot q  = − cot(−q)

    Addition formulas

sin(a + b) = sin a cos b  + cos a sin b

sin(a − b) = sin a cos b  − cos a sin b

cos(a + b) = cos a cos b  − sin a sin b

cos(a − b) = cos a cos b  + sin a sin b

   Double-angle formulas

sin 2a  = 2 sin a cos a

            cos 2a  = cos² a  − sin² a   =   2 cos² a  − 1   =   1 − 2sin² a

   Half-angle formulas

            sin² a  = (1 − cos 2a )/2

            cos² a  = (1 + cos 2a )/2