Mathematics: Show work on these ! find the radian measure of an angle of -280 degrees. find the degree measure of an angle of 3pi/5 radians. find the exact values of cos(3pi/4 radians) and sin(3pi/4 radians).

there are many angles what angles are you talking aboutStep-by-step explanation:...

Show work on these ! find the radian measure of an

Ответ:

petriajack5543

05.01.2022

Mathematics

- 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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Show work on these !

find the radian measure of an angle of -280 degrees.

find the degree measure of an angle of 3pi/5 radians.

find the exact values of cos(3pi/4 radians) and sin(3pi/4 radians).

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