Thread: Sketching Angle in Standard Position

This is an example from the resource I am learning trig from. Where they are sketching angles in standard position. They are showing an example of -pi/4 in orange. Isn't this incorrect? the way they have this marked looks much closer to -1/3 instead of -1/4.

This is the example in question.
https://imgur.com/l8OfhDM

But then here is another example how they sketch
https://imgur.com/azQ9pMF

Originally Posted by cmf0106

This is an example from the resource I am learning trig from. Where they are sketching angles in standard position. They are showing an example of -pi/4 in orange. Isn't this incorrect? the way they have this marked looks much closer to -1/3 instead of -1/4.

Attachment 38861

pi/3 rad --> 60 degrees. This is more than 1/2 way between 0 and pi/2 --> 90 degrees.

pi/4 rad --> 45 degrees. Looks good to me.

-Dan

Originally Posted by cmf0106

But then here is another example how they sketch
https://imgur.com/azQ9pMF

You have done this in both posts.
You have written $\Large{\color{red}{\dfrac{\pi}{3}\text{ or }\dfrac{1}{3}}}$ and that is wrong.

$\dfrac{\pi}{3}~\&~\dfrac{1}{3}$ are two different measures.
One third is different from pi divided by three.

Study this webpage.

When I put down 1/3 its short hand for "1/3 pi" is that still wrong?

Originally Posted by cmf0106

When I put down 1/3 its short hand for "1/3 pi" is that still wrong?

First, there is no short hand in mathematics. If you were in my class I would expect the grader to mark your paper completely incorrect if you did that. Moreover, you have included degrees in some of your images. WHY? Because a radian is the measure of an angle of a central angle in a circle that subtends an arc of length equal to the radius of the circle. Therefore clearly a radian is a number, I don't know what a degree is.

Huh. I never saw the second graph. Must have been added after I made my response.

-Dan