Further Trig: Prelim extension math theory

State the base cos double angle formula:

cos2x = cos²x - sin²x

State all other versions of the cos double angle formula:

cos2x = 2cos² - 1

cos2x = 1 - sin²x

cos2x = ½ + ½ cos2x

sin²x = ½ - ½ cos2x

State the sin double angle formula:

sin2x = 2sinxcosx

State the cofunction identity for tan(a-b):

tan(a-b) = tana - tanb / 1+tanatanb

How do you convert degrees to radians?

By multiplying the degrees by pi/180

At what angles is tanx undefined at?

At 90^o and 270^o

At what angles does tanx = 1

At 45^o (pi/4 radians)

At what anges does sinx = ½ ?

At 30^o and 150^o

At what angles does cosx equal -1/2?

At 120^o and 240^o (2pi/3 and 4pi/3)

At what angles does cosx= 0

At 90^o and 270^o

At what angles does cosx= ½ ?

At 60^o and 300^o

At what angles does sinx = 0?

At 0^o, 180^o, and 360^o

State the cofunction identity for sin(a-b):

sin(a-b) = sinacosb - sinbcosa

State the tan double angle formula:

tan2x = 2tanx/ 1 - tan²x

State the cofunction identity for tan(a+b):

tan(a+b) = tana + tanb/ 1-tanatanb

State the cofunction identity for cos(a-b)

cos(a-b) = cosacosb + sinasinb

State the cofunction identity for cos(a+b):

cos(a+b) = cosacosb - sinasinb

State the cofunction identity for sin(a+b)

sin(a+b) = sinacosb + cosasinb