SOLUTION: What is the value of cos−1 ⁡(−√2/2) in Quadrant II? cos−1⁡ (−√2/2)= __________°

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Question 1062978: What is the value of cos−1 ⁡(−√2/2) in Quadrant II?
cos−1⁡ (−√2/2)= __________°

Found 3 solutions by Alan3354, josmiceli, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You could find the answer with a calculator.
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I recommend you learn the unit circle, tho.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+arc+cos%28+-sqrt%282%29%2F2+%29+ in quadrant 2
( I like to write it this way )
This is the same as:
+arc+cos%28+-1%2Fsqrt%282%29%29+%29+
Since
+1%5E2+%2B+1%5E2+=+sqrt%282%29%5E2+
+2+=+2+
The terminal point is ( -1,1 )
This gives me an angle of +3%2Api%2F4+
+arc+cos%28+-sqrt%282%29%2F2+%29+=+3%2Api%2F4+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
What is the value of cos−1 ⁡(−√2/2) in Quadrant II?
cos−1⁡ (−√2/2)= __________°
In the 1st quadrant: cos%5E-+1+%28sqrt%282%29%2F2%29+=+45%5Eo
In the 2nd quadrant, where cos < 0, the reference angle of matrix%281%2C1%2C+cos%5E-+1+%28-+sqrt%282%29%2F2%29+=+90%5Eo+%2B+45%5Eo+=+135%5Eo%29
Converting 135%5Eo to, radians, we get: highlight_green%28matrix%281%2C3%2C+135+%2A+%28pi%2F180%29%2C+%22=%22%2C+3pi%2F4%29%29