Addition and subtraction of angles and the double angle formula

Addition of angles formulae:               
cos(a + b) = cosacosb   – sinasinb      
sin(a + b) = cosasinb   + sinacosb          

Subtraction of angles formulae:
cos(a – b) = cosacosb   + sinasinb
sin(a – b) = sinacosb  - cosasinb

The double angle formulae:
cos(2a) = cos²a - sin²a
sin(2a) = 2cosasina

For the tangents of the new angles, divide sine by cosine.

Consider two angles a and b, with the following sine and cosine values.

sina = 1/3 and cosa = 2sqrt(2)/3

sinb = 2/3 and cosb = sqrt(5)/3

Find the following values as exact numbers.

sin(a + b)
cos(a + b)
tan(a + b)


sin(a - b)
cos(a - b)
tan(a - b)



sin(2a)
cos(2a)
tan(2a)


Answers in the comments.


 

Notes for Homework 6, due March 6

Notes for double angle and addition and subtraction of angles

Notes for Homework 6, due March 5

Notes for the double angle formulae and the addition and subtraction of angles

Notes on trig identities