radian measure of angle in standard position

[sayyadina]

Find the radian measure of an angle in standard position within (0, 2pi) that is coterminal to each angle given.

I've been able to solve problems where I'm given 8pi, 7pi/2 or -pi/2, but I can't get the right answer if I'm given -7pi/5 or -9pi/4.

I had a video walkthrough for -pi/4, to show me how to do this one. It basically said to do -pi/4 + 2pi = -pi/4 + 8pi/4 = 7pi/4.

I understand that coterminal angles may go around the circle differently, but they end on the same ray.

I tried doing this for some of the other problems (adding 2pi), but it didn't work. So, then I thought I'd convert to degrees, determine how many revolutions are occurring, and convert whatever the difference is back to radian since that would be the answer.

So if I'm given 8pi/3....

(8pi/3)(180/pi)=480 degrees

480-360=120

120(pi/180)= 2pi/3

And it turns out that 2pi/3 is right.

But then I go to solve -9pi/4......

-9pi/4 (180/4)= -405

405-360= 45 or really -45

-45(pi/180)=-pi/4 (which is wrong)

Then I try the other way......

-9pi/4 + 2pi = -9pi/4 + 8pi/4 = -pi/4

The book says the answer is 7pi/4.......but given the little explanation the book gives, and the video walkthrough, I have no idea how to get that.


What am I doing wrong?

 

[Deleted member 4993]

Find the radian measure of an angle in standard position within (0, 2pi) that is coterminal to each angle given.

I've been able to solve problems where I'm given 8pi, 7pi/2 or -pi/2, but I can't get the right answer if I'm given -7pi/5 or -9pi/4.

I had a video walkthrough for -pi/4, to show me how to do this one. It basically said to do -pi/4 + 2pi = -pi/4 + 8pi/4 = 7pi/4.

I understand that coterminal angles may go around the circle differently, but they end on the same ray.

I tried doing this for some of the other problems (adding 2pi), but it didn't work. So, then I thought I'd convert to degrees, determine how many revolutions are occurring, and convert whatever the difference is back to radian since that would be the answer.

So if I'm given 8pi/3....

(8pi/3)(180/pi)=480 degrees

480-360=120

120(pi/180)= 2pi/3

And it turns out that 2pi/3 is right.

But then I go to solve -9pi/4......

-9pi/4 (180/4)= -405

405-360= 45 or really -45

-45(pi/180)=-pi/4 (which is wrong)

Then I try the other way......

-9pi/4 + 2pi = -9pi/4 + 8pi/4 = -pi/4

The book says the answer is 7pi/4.......but given the little explanation the book gives, and the video walkthrough, I have no idea how to get that.


What am I doing wrong?

You understand that the answer Θ should be such that 0 ≤ Θ ≤ 2*π

Your answer was -π/4 < 0, hence not within the required domain which is 0 ≤ Θ ≤ 2*π

so you need to add 2*π again to bring it to the required domain.

-π/4 + 2π = 7π/4