Easy trig question that I am having trouble with

  • Thread starter nicksbyman
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In summary: No, the radius is not 7. The unit circle applies to all trig functions. the -7 in the is case is better thought of as -1/7 which is the sine of the angle.
  • #1
nicksbyman
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Homework Statement



3-2csc(x) = 17

Homework Equations



N/A

The Attempt at a Solution



3-2csc(x)= 17
-2csc(x) = 14
csc(x) = -7

cscˆ-1(-7) = x

x = -.14 radians. This is not the correct answer. The correct answerS ARE 3.28 or 6.24 radians. I am beyond confused. Please help :)

Thanks
 
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  • #2
nicksbyman said:

Homework Statement



3-2csc(x) = 17

Homework Equations



N/A

The Attempt at a Solution



3-2csc(x)= 17
-2csc(x) = 14
csc(x) = -7

cscˆ-1(-7) = x

x = -.14 radians. This is not the correct answer. The correct answerS ARE 3.28 or 6.24 radians. I am beyond confused. Please help :)

Thanks

Do you mean 3.28 and 6.14?
 
  • #3
stevenb said:
Do you mean 3.28 and 6.14?

Yes, sorry I copied it wrong. But how did you get that?
 
  • #4
nicksbyman said:
Yes, sorry I copied it wrong. But how did you get that?

OK, think about the unit circle.

The answer of -.14 is the same as 6.14 because they are different by 2pi (ignoring round off error, of course).

The other answer comes from thinking about any other places on the unit circle that might have the same value of csc. Since csc=1/sin, then you need to think about the unit circle and the another place where the sine is the same value.
 
  • #5
stevenb said:
OK, think about the unit circle.

The answer of -.14 is the same as 6.14 because they are different by 2pi (ignoring round off error, of course).

The other answer comes from thinking about any other places on the unit circle that might have the same value of csc. Since csc=1/sin, then you need to think about the unit circle and the another place where the sine is the same value.

That's the perfect response :D I just spent the last 15 minutes or so toiling with that question (I'm a slow learner) and I finally got it.

Thanks again.

P.S. Correct me if I'm wrong, but we aren't dealing with the unit circle here right? We only deal with the unit circle when the radius is 1 I thought. In this case, the radius is 7. That is, we are dealing with a circle, but not the unit circle.
 
  • #6
nicksbyman said:
P.S. Correct me if I'm wrong, but we aren't dealing with the unit circle here right? We only deal with the unit circle when the radius is 1 I thought. In this case, the radius is 7. That is, we are dealing with a circle, but not the unit circle.

No, the radius is not 7. The unit circle applies to all trig functions. the -7 in the is case is better thought of as -1/7 which is the sine of the angle.

Personally, I always find secant and cosecant to be confusing, and prefer to think in terms of sine and cosine. It's just a preference, but it may be one that helps you.
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving right triangles and is also used in fields such as physics, engineering, and astronomy.

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3. What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in trigonometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

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