Trigonometric functions of the unit cirlce

In summary, the problem is to find the csc of an angle in radians, specifically -2pi/3 or -120 degrees. The problem solver got -2sqrt.(3)/3 but the answer in the back of the book is -2sqrt.(3)/2. The confusion arises because the sin is -sqrt.(3)/2, which is correct, so shouldn't the csc be the reciprocal of sin, 1/sin theta? However, the book's answer is incorrect and the correct answer is -2sqrt.(3)/3. The book has made multiple errors, causing confusion for the problem solver.
  • #1
AznBoi
471
0
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!
 
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  • #2
Your book is wrong. [tex] cosec(\frac{-2\pi}{3}) = \frac{-2\sqrt{3}}{3} [/tex]
 
  • #3
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! =]
 

Related to Trigonometric functions of the unit cirlce

What are the trigonometric functions of the unit circle?

The trigonometric functions of the unit circle are sine, cosine, tangent, cotangent, secant, and cosecant. These functions represent the ratios of the sides of a right triangle in the unit circle.

How do you use the unit circle to find trigonometric functions?

To find trigonometric functions using the unit circle, you first need to identify the reference angle, which is the angle between the terminal side of the angle and the x-axis. Then, you can use the ratios of the sides of the right triangle in the unit circle to determine the values of the trigonometric functions.

What are the values of the trigonometric functions at key angles on the unit circle?

The values of the trigonometric functions at key angles on the unit circle are as follows:

  • At 0 degrees, all trigonometric functions have a value of 0.
  • At 30 degrees, sine is 1/2, cosine is √3/2, tangent is 1/√3, cotangent is √3, secant is 2/√3, and cosecant is 2.
  • At 45 degrees, sine and cosine are both 1/√2, tangent is 1, cotangent is 1, secant and cosecant are both √2.
  • At 60 degrees, sine is √3/2, cosine is 1/2, tangent is √3, cotangent is 1/√3, secant is 2, and cosecant is 2/√3.
  • At 90 degrees, sine is 1, cosine is 0, tangent is undefined, cotangent is 0, secant is undefined, and cosecant is 1.

How can the unit circle be used to solve trigonometric equations?

The unit circle can be used to solve trigonometric equations by first converting them to equations involving the trigonometric functions of the unit circle. Then, the values of these functions at key angles can be used to solve for the variable in the equation.

What are some real-world applications of trigonometric functions of the unit circle?

Trigonometric functions of the unit circle have many real-world applications, including in navigation, astronomy, and engineering. They can be used to calculate distances, angles, and heights in various fields such as surveying, physics, and architecture.

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