Answer:
[tex]-\frac{\sqrt2}{2} \\[/tex] or exact is −0.70710678...
Step-by-step explanation:
Getting the point!
- If we look at the unit circle and we find [tex]-\frac{3\pi }{4}[/tex] we see it is in the 3rd quadrant.
- We know that all points in the 3rd quadrant have both negative x and negative y values.
- We know that all radians with the base of 4 on the unit circle have the points of [tex](\frac{\sqrt{2}}{2} ,\frac{\sqrt{2}}{2})[/tex]
- Because we are in the 3rd quadrant and both x and y are negative we know the point of [tex]-\frac{3\pi }{4}[/tex] is [tex](-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2})[/tex]
Finding the sin!
- Because we know that sin is asking us for the y value
- We can just look at the point and find the y value!
- the y value is [tex]-\frac{\sqrt2}{2} \\[/tex]
- Because this fraction does not need to be rationalized we are good!
- Use a calculator to find the exact value and you get -0.70710678...
- The final answer is [tex]-\frac{\sqrt2}{2} \\[/tex] or exact is −0.70710678...
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