# Math Help - Trigonometry Reduction Identity

1. ## Trigonometry Reduction Identity

y = -sin x - cos x
It says to use the reduction identity to graph each equation.
I have absolutely no clue how to do this. I recall my teacher saying he doesn't like to use the reduction identity given in the book so he changes the form to m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x). Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.

2. y=-senx-cosx
y=-(senx+cosx)
y=-sqrt(2){[(sqrt(2).senx)/2]+[(sqrt(2).cosx)/2]}
y=-sqrt(2).sen(45+x)
you will have a function that ranges from -sqrt(2) to sqrt(2);translated to the left by 45 degrees and being the reflex of the function y=sqrt(2).sen(45+x)
hope it helps
=)

3. Originally Posted by hellojellojw
m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x).
Do you know how to expand sin (a + b) ?

Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.
Compare the coefficients of m*sin(x + y) and (-sin x - cos x)

4. Originally Posted by songoku
Do you know how to expand sin (a + b) ?

Compare the coefficients of m*sin(x + y) and (-sin x - cos x)
Yes I know the addition laws.

The most I'm confused about is going from this msin(x)cos(y) + mcos(y)sin(x)
to mcosy = -1 and msiny = -1.

5. Originally Posted by hellojellojw
m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x). Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.
y = - sin x - cos x
= m*sin ( x + y )
= msin(x)cos(y) + mcos(y)sin(x)

Then, - sin x - cos x = msin(x)cos(y) + mcos(y)sin(x)

Compare the left and right side of the equation

6. Originally Posted by songoku
y = - sin x - cos x
= m*sin ( x + y )
= msin(x)cos(y) + mcos(y)sin(x)

Then, - sin x - cos x = msin(x)cos(y) + mcos(y)sin(x)

Compare the left and right side of the equation
ahh I see now I think.
I just set -sinx = msinxcosy and got mcosy = -1.
Thanks.

7. Oh yeah and one more quick question. How is
-sin x - cos x = m sin(x + y)
Like how do you come up with that?

8. it's because we don't have any formulas for sin x + cos y.

There are formulas for sin x + sin y, sin x - sin y, cos x + cos y, cos x - cos y, but not sin x + cos y

So, we just set that sin x + cos x = m sin(x + y) in order to simplify it.
You can also set sin x + cos x = m sin(x - y), or sin x + cos x = m cos(x + y), or sin x + cos x = m cos(x - y).
The process will be different, but the final answer will be the same if you want to find the exact value of x