Trigonometric functions of the unit cirlce

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SUMMARY

The discussion centers on calculating the cosecant (csc) of the angle t = -2π/3 radians, which is equivalent to -120 degrees. The user initially calculated csc(-2π/3) as -2√3/3, while the textbook provided the answer as -2√3/2. The user correctly identified that the sine of -2π/3 is -√3/2, leading to the conclusion that the cosecant should indeed be the reciprocal of sine, resulting in -2√3/3. The discrepancy indicates an error in the textbook.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosecant and sine.
  • Knowledge of angle conversion between radians and degrees.
  • Familiarity with the unit circle and its properties.
  • Basic algebra skills for manipulating square roots and fractions.
NEXT STEPS
  • Review the properties of trigonometric functions on the unit circle.
  • Practice calculating cosecant values for various angles in radians.
  • Explore common errors in trigonometric calculations and how to avoid them.
  • Study the relationship between sine and cosecant in greater detail.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric functions, and anyone seeking to clarify misconceptions about cosecant and sine calculations.

AznBoi
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I just came across a problem that wants you to solve for csc of an angle in radians... However, I'm confused about the answer given.

Here is the problem:

Find the csc when t=-2pi/3, which is equivalent to -120 degrees right?

I got -2sqrt.(3)/3 but the answer in the back is -2sqrt.(3)/2 Why is it a 2 instead of a three??

The sin is -sqrt.(3)/2 and it is correct, so shouldn't the csc be the reciprocal of sin?? 1/sin theta?? so 1/(-2sqrt.(3)/3)?

Thanks!
 
Physics news on Phys.org
Your book is wrong. [tex]cosec(\frac{-2\pi}{3}) = \frac{-2\sqrt{3}}{3}[/tex]
 
wow... I think I've actually seen quite a few with 2's as the denominator. I'm pretty sure that I was right and the book was wrong. I'm astonished though, this book sucks! =/


Thanks for helping me check btw! =]
 

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