Trig and Inequality question: Find the θ to 4 significant digits for 0 ≤ θ < 2π if tan θ = -0.7434

[I_Just_Want_To_Pass]

I'm a bit stuck on this question: "Find the θ to 4 significant digits for 0 ≤ θ < 2π if tan θ = -0.7434".
I thought θ = -36.627 but that was less than 0 and goes against the inequality equation, I'm a bit stuck

 

[limiTS]

Go all the way around the circle and you'll get to the same angle. That is, add 360 degrees to -36.627 degrees and you'll get an angle within the bounds.

You could instead add 180 degrees.

But you might want to keep everything in radians.

 

[Harry_the_cat]

The answer is required in radians as the question states \(\displaystyle 0 \leq \theta <2\pi\).

If the answer was to be in degrees, it would state \(\displaystyle 0^\circ \leq \theta <360^\circ\).

There are two answers within those boundaries - one in the second quadrant and the other in the fourth quadrant. (Do you know the ASTC rule?)

Your calculator has given you the answer in degrees in the fourth quadrant. To get the answers within your boundaries, add \(\displaystyle 180^\circ\) (to get the solution in the second quadrant) and add \(\displaystyle 360^\circ\) (to get the solution in the fourth quadrant). To convert to radians, multiply your answers by \(\displaystyle \frac{\pi}{180^\circ}\).

It would be easier if you worked in radians from the start. Your calculator should be in RAD mode (radian mode).

\(\displaystyle \tan^{-1}(-0.7434) \approx -0.63926\).

Now, to find the two solutions within the boundaries, add \(\displaystyle \pi\) and \(\displaystyle 2\pi\).

Don't forget to round off your final solutions to 4 decimal places as stated in the question.

 

[The Highlander]

I'm a bit stuck on this question: "Find the θ to 4 significant digits for 0 ≤ θ < 2π if tan θ = -0.7434".
I thought θ = -36.627 but that was less than 0 and goes against the inequality equation, I'm a bit stuck

Everything you've been told (above) is good, except...

Don't forget to round off your final solutions to 4 decimal places as stated in the question.

You should not round your answer to "4 decimal places" as that is not what was "stated in the question" (if you have reproduced it accurately)!
The question instructs you to "Find the θ to 4 significant digits" which is a quite different thing.

Please post your final answer(s) so that we can see if you've tackled the question successfully.

 

[Harry_the_cat]

Woops! Yes it says 4 significant figures not 4 decimal places. Sorry about that.

 

[I_Just_Want_To_Pass]

Everything you've been told (above) is good, except...

You should not round your answer to "4 decimal places" as that is not what was "stated in the question" (if you have reproduced it accurately)!
The question instructs you to "Find the θ to 4 significant digits" which is a quite different thing.

Please post your final answer(s) so that we can see if you've tackled the question successfully.

Sorry, for the wait, this is my first time using this site, but the answer I got was -36.6271 and 36.6271

 

[The Highlander]

Sorry, for the wait, this is my first time using this site, but the answer I got was -36.6271 and 36.6271

You, yourself, pointed out that the negative answer was outside the given boundaries and the tangent of 36.6271° is not -0.7434 so both your answers are wrong!

However, you were given good advice on how to interpret the negative answer (-36.6271°) which, unfortunately, you do not appear to have paid attention to.

Furthermore, you still appear to be working to four decimal places which, again, the question told you not to do (your answers need to be to 4 significant digits!) and they should also be in radian measure (not degrees).

So yo need to:-

a) Go back and read Post # 3 carefully, then follow the advice given there.​

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b) Change your calculator to Radian mode and​

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c) Post your answers to 4 significant digits.​

If you are really struggling with any of those then post, in detail, what attempts you have made (a picture will suffice) and further help will be provided if necessary. ?

(If you sketch out the possible angles on a unit circle that may help you to get the correct answers.)

 

[The Highlander]

Maybe this (rough) sketch will aid your understanding?

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Note that in each case the "angle" is 45° (\(\displaystyle \frac{\pi}{4}\) radians) away from the x-axis

 

[khansaheb]

I'm a bit stuck on this question: "Find the θ to 4 significant digits for 0 ≤ θ < 2π if tan θ = -0.7434".
I thought θ = -36.627 but that was less than 0 and goes against the inequality equation, I'm a bit stuck

Do you know the definition of significant digits?

If you are not sure, please read the following:

Significant figures - Wikipedia

en.wikipedia.org

 

[The Highlander]

Go all the way around the circle and you'll get to the same angle. That is, add 360 degrees to -36.627 degrees and you'll get an angle within the bounds.

You could instead add 180 degrees.

But you might want to keep everything in radians.

It should be pointed out (for the sake of accuracy) that when you "Go all the way around the circle" you do not get to the same angle.

For example, 30° and 390° have the same reference angle (30°) and (because they are coterminal) share all the same trigonometric ratios but they are not the same angle!

Whereas, -30°, 150° and 330°, again having the same reference angle (30°), are all different angles but (since they all lie in either the 2nd or 4th quadrant) they share the same Tangent Ratio!
(Another big hint to @I_Just_Want_To_Pass ?)

 

[The Highlander]

Do you know the definition of significant digits?

If you are not sure, please read the following:

Significant figures - Wikipedia

en.wikipedia.org

@I_Just_Want_To_Pass,

If you find the Wikipedia entry (on Sig Figs) at all confusing then here is the "summary" sheet I get my pupils to copy down...

​

Alternatively, you might wish to watch my PowerPoint presentation on the subject: "Scientific Notation & Sig Figs.ppsx" (attached).

I'm afraid the specific section dealing with Significant Figures is right at the end but it would do you no harm to watch the whole thing.

NB: After downloading the attached file ("Scientific Notation & Sig Figs.txt") you will need to change its file extension from ".txt" to ".ppsx" so that it will open correctly (always assuming, of course, that you do have software installed that allows you to Open PowerPoint presentations).