Answer:
- 14π/9; 108°; -√2/2; √2/2
Step-by-step explanation:
To convert from degrees to radians, use the unit multiplier [tex]\frac{\pi }{180}[/tex]
In equation form that will look like this:
- 280° × [tex]\frac{\pi }{180}[/tex]
Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have [tex]-\frac{14\pi }{9}[/tex]
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:
[tex]\frac{3\pi }{5}[/tex] × [tex]\frac{180}{\pi }[/tex]
Simplifying all of that and canceling out the radians gives you 108°.
The third one requires the reference angle of [tex]\frac{3\pi }{4}[/tex].
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 [tex]-\frac{1}{\sqrt{2} }[/tex]
which rationalizes to [tex]-\frac{\sqrt{2} }{2}[/tex]
The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized, [tex]\frac{\sqrt{2} }{2}[/tex]
And you're done!!!
