Easy trig question that I am having trouble with

[nicksbyman]

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

 

[stevenb]

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?

 

[nicksbyman]

Do you mean 3.28 and 6.14?

Yes, sorry I copied it wrong. But how did you get that?

 

[stevenb]

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.

 

[nicksbyman]

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.

 

[stevenb]

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.