2 Answers:
Choice A
Choice B
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Explanation:
Refer to the unit circle shown below.
The angle 3pi/4 radians is equivalent to 135 degrees.
The angle is in Q2.
The reference angle for stuff in Q2 is 180 - theta = 180 - 135 = 45 degrees. This makes choice B one of the answers. It rules out choices C and D.
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The terminal point for this angle is [tex]\left(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)[/tex] which those coordinates represent the cosine and sine of theta in that order.
[tex]x = \cos(\theta) = -\frac{\sqrt{2}}{2}\\\\y= \sin(\theta) = \frac{\sqrt{2}}{2}[/tex]
Dividing sine over cosine gets us [tex]\tan(\theta) = -1[/tex]
These facts show that choice A is the other answer. Choices E and F are false.