Answer:
Step-by-step explanation:
You have to use the half angle identities for trig. You will also need access to a unit circle with radian measures of angles. The identity for the half angle for sin is
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To use a half angle identity, the trick is to rewrite the half angle so that when you bring up that 2 in the denominator and flip it to multiply you get back the angle you started with. Our angle is 7π/8. Divide the 8 by 2 and you get your angle to be in the form
Note that when you bring up the 2 and flip it to multiply you get back 7π/8.
Do you see that? For the formula, then, our angle theta is 7π/4. If you look to the unit circle, you see that the cosine of that angle is √2/2. Filling in the formula:
Get a common denominator up on top there and simplify:
You'll bring up that bottom 2 and flip it to multiply:
Simplify to get
Since 4 is a perfect square, the final simplification will be to pull it out as a 2:
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And you're all done! Easy if you know how to use the formula and the unit circle.