sin(x+x) can also be expressed as...

sin(2x)

sin(x-y)

sin(x)cos(y)-cos(x)sin(y)

if it is addition of the angles

Sin(x+y)

Sin(x)Cos(y)+Cos(x)Sin(y)

if we want to simplify, we get...

2sin(x)cos(y)

cos(x+x)

cos(2x)

cos(x)cos(x)-sin(x)sin(x)

Simplify

cos^2(x)-sin2(x)

you can also do this...

cos(2x)= 2cos^2(x)-1

which we can get by replacing the (sin^2(X)) with our knowledge of this equation.

sin^{2(x)+cos2(x)=1}

You can do this again except by replacing cos^2(x)

These three cos angle identities are all equal.

Tan(x+y)

Tan(x)+Tan(y)

1-tab(x)tan(y)

Evaluating the values of a trig function

Sin(120)

Sin(90+30)

Sin(90)Cos(30)+Cos(90)Sin(90)

(1)(root3/2) + (0)(sin90)

Root3/2

Finding the angle of a sin trig function

Sin(90)Cos(30)+Cos(90)Sin(90)

Sin(90 +30)

Sin(120)

Now circle trig and radians

1pi=180

So evaluate

5pi/4

225 degrees

The circle trig (by now you should realize why we should avoid blatant memorization)

-Positive angles are counterclockwise -negative angles are clockwise

Sin(.75pi) Sin(135) Which is in quadrant II So we have reference angle of 45 Meaning that if you know sin45 which is Root2/2 Then you also know sin(135) equals root2/2

But if the y value was negative then we know that the trig function is either in 3 or 4 and in this case if a function has a reference angle of 45 in quadrant 3 or 4 then root2/2 is negative.

If you can't understand still then try looking up circle trig.

There are other things left out that I have not explained like trig Pythagorean equations and half angle trig equations which u might need to look up.

I hope this helped and that you take a look at this because I wrote this during my history class. Ps ignore the bad grammar.

Source: HS student who likes math.