SOLUTION: Find the point on the terminal side of θ = -(3π/4) that has an x coordinate of -1.

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Question 1131310: Find the point on the terminal side of θ = -(3π/4) that has an x coordinate of -1.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
theta=+%28-3pi%2F4%29=+-135 ° or 225 °
sin%28-135+%29+=+sin%28225+%29
cos%28-135+%29+=+cos%28225+%29
First you must know that:
x=r%2Acos%28theta%29 =>where cos%28-%283pi%2F4%29%29=-1%2Fsqrt%282%29=-sqrt%282%29%2F2
y=r%2Asin%28theta%29 => where sin%28-%283pi%2F4%29%29=-1%2Fsqrt%282%29=-sqrt%282%29%2F2
We are given that theta=-3pi%2F4, x=-1
So, first plug x and theta into the first formula to get the value of "r"
-1=r%2Acos%28-3pi%2F4%29
-1=r%28-sqrt%282%29+%2F2%29
-1%282%29=r%2A%28-sqrt%28+2%29%29
-2=r%2A%28-sqrt%282%29%29
r=sqrt%282%29

Now plug in "r"  and  theta into the second formula to get the value of y
y=r%2Asin%28theta%29
y=sqrt%282%29%2Asin%28-3pi%2F4%29
y=sqrt%282%29%2A%28-sqrt%282%29%2F2%29
y=%28-%28sqrt%282%29%29%5E2%2F2%29
y=-2%2F2
y=-1
So, your terminal point will be (-1,-1)