How can I determine the biggest trig value without a calculator?

[mathdad]

How do I determine which trig value is bigger or smaller without using a calculator?

Sample:

Which is bigger: cos 2 or sin 2?

 

[MarkFL]

In which quadrant is an angle of 2 radians?

 

[mathdad]

Angle 2 radians in degrees is 114.6°. We are in quadrant 2.

In quadrant 2, cosine is negative and sine is positive.

So, can I conclude by saying that sin 2 > cos 2?

 

[MarkFL]

Angle 2 radians in degrees is 114.6°. We are in quadrant 2.

In quadrant 2, cosine is negative and sine is positive.

So, can I conclude by saying that sin 2 > cos 2?

Yes, we know the angle is in quadrant II since:

$$\frac{\pi}{2}<2<\pi$$

And so your result follows. :)

 

[mathdad]

This is interesting. I took a course by the title Math 185 at NYC TECHNICAL COLLEGE in the early 1990s. The course covers Algebra 2 and Trig. The professor never introduced this material. In fact, he decided to skip the entire unit circle and how it works. I am going to use the David Cohen textbook to learn all the trig I missed in my youth. I AM A VICTIM OF NYC PUBLIC SCHOOL EDUCATION.