Unit 6 Solving Trigonometry Formulas

quick review:

related angle identities (involving 0, pi, and two pi):

the first picture is a circle on a graph, with point P as the starting point, and P' (P prime) as the new point. basically, you look at the original x or y value (depending on what you're looking at) and then you look at the new respective x or y value, and see how it has changed. er.. as you look at the graph and then the box below with the identities, it should make more sense. you should be able to derive these identites yourself, from the graphs...but if you can not remember how the graphs work, then it would be better to memorize.

this is the graph:

these are the identites derived from the graph above.

this is a graph showing a reflection about the origin:

and it's corresponding identites:

where two pi minus theta... or reflection along x-axis

corresponding identities:

same graph as above, but this one shows the even and odd functions:

even/odd function identites:

these are co- related angle identities (so involving 0, 90 and 270 degrees)
reflection along y = x axis

corresponding identites, y = x axis :

this one is on the other side...

these two are for 270 degrees... same idea, so no graph =D

addition and subtraction of angle formulas:


addition of cos:

subtration of cos: note the different signs, and that cos and cos are together, sin with sin.(always for cos)

addition of sin, note the signs are the same, but sin is with cos.

subtraction of sin: for sin, the sign is always the same, and it is always sin with cos.

addition of tan: the top signs are always the same, the bottom are always opposite.

subtration of tan: top signs same, bottom opposite.

Double and half angle formulas:

for sin:

cos has three identites for double angles:

half angle formula for cos:

double angle formula for tan:

half angle for tan: (sorry, i dont know why it's sideways)