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Digiron [165]
3 years ago
8

Please show work on these questions!!!

Mathematics
1 answer:
asambeis [7]3 years ago
7 0

Answer:

- 14π/9; 108°; -√2/2; √2/2

Step-by-step explanation:

To convert from degrees to radians, use the unit multiplier \frac{\pi }{180}

In equation form that will look like this:

- 280° × \frac{\pi }{180}

Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have -\frac{14\pi }{9}

The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians.  That equation looks like this:

\frac{3\pi }{5} × \frac{180}{\pi }

Simplifying all of that and canceling out the radians gives you 108°.

The third one requires the reference angle of \frac{3\pi }{4}.

If you use the same method as above, we find that that angle in degrees is 135°.  That angle is in QII and has a reference angle of 45 degrees.  The Pythagorean triple for a 45-45-90 is (1, 1, √2).  But the first "1" there is negative because x is negative in QII.  So the cosine of this angle, side adjacent over hypotenuse, is -\frac{1}{\sqrt{2} }

which rationalizes to -\frac{\sqrt{2} }{2}

The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized, \frac{\sqrt{2} }{2}

And you're done!!!

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