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

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To determine which trigonometric value is larger without a calculator, one can analyze the angle's quadrant. For an angle of 2 radians, which is approximately 114.6 degrees, it lies in the second quadrant where sine is positive and cosine is negative. Thus, it can be concluded that sin 2 is greater than cos 2. The discussion highlights the importance of understanding the unit circle and quadrants in trigonometry. Additionally, the user reflects on their educational experience and plans to study trigonometry more thoroughly.
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How do I determine which trig value is bigger or smaller without using a calculator?

Sample:

Which is bigger: cos 2 or sin 2?
 
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In which quadrant is an angle of 2 radians?
 
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?
 
RTCNTC said:
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. :)
 
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.
 
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