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

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In summary, the conversation discusses determining which trig value is bigger or smaller without using a calculator. The participants also touch on the concepts of quadrant and angle measurement in degrees. They conclude that in quadrant 2, sine is greater than cosine. The speaker also mentions their past experience with a math course and their plan to revisit trigonometry using a textbook.
  • #1
mathdad
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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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  • #2
In which quadrant is an angle of 2 radians?
 
  • #3
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?
 
  • #4
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:

\(\displaystyle \frac{\pi}{2}<2<\pi\)

And so your result follows. :)
 
  • #5
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.
 

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

What is the biggest trig value?

The biggest trig value is infinity. This is because the trigonometric functions (sine, cosine, tangent) can approach infinity as the input value approaches certain values.

What is the biggest value for sine?

The biggest value for sine is 1. This occurs when the angle is 90 degrees (π/2 radians).

What is the biggest value for cosine?

The biggest value for cosine is 1. This occurs when the angle is 0 degrees (0 radians).

What is the biggest value for tangent?

The biggest value for tangent is infinity. This occurs when the angle is 90 degrees (π/2 radians).

Why is the biggest trig value infinity?

This is because the trigonometric functions are defined as ratios of lengths in a triangle, and as the angle approaches certain values, the ratio of the sides becomes infinitely large.

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