I don’t understand what my Calculus hw question is asking of me…not looking for answers, just guidence.

Trigonometry – The signs of trigonometric functions
Trigonometry – The signs of trigonometric functions

I really don’t understand what I am supposed to do. I understand cos = opp/hyp…etc. But my book doesn’t give me enough info to figure this question out, nor do I really understand what it is asking me to do. Could someone please explain this? I am fine with you giving me an answer for maybe sin0, but please do not give me all the answers, I need to learn this not be giving the answers. Yes this is hw, don’t blast me…I want to learn.

I don’t understand what my Calculus hw question is asking of me…not looking for answers, just guidence.

  • 3$\begingroup$ You’re supposed to substitute $\theta = -\frac{3\pi}{4}$ into $\sin\theta$, $\cos\theta$, $\tan\theta$, etc. and put the corresponding values in the boxes. $\endgroup$ Jul 2, 2015 at 1:43
  • 1$\begingroup$ I still don’t understand. Do you mean im supposed to do sin(3π/4)? If so, I have no documentation on how to do this, nor can I find any. $\endgroup$ Jul 2, 2015 at 1:45
  • $\begingroup$ Yes that is correct. $\endgroup$ Jul 2, 2015 at 1:46
  • $\begingroup$ Use the $x, y,$ and $r$ definitions of trigonometric functions. The angle of $\theta = 3\pi/4$ corresponds to the point $(x, y) = (-1/\sqrt{2}, 1/\sqrt{2})$ on the unit circle. And yes, you’ll compute $\sin(3\pi/4)$, and $\cos(3\pi/4)$, and etc. $\endgroup$– pjs36Jul 2, 2015 at 1:46
  • 3$\begingroup$ The opp/hyp definition that you mentioned makes sense only for angles that can occur in a right triangle, not for obtuse angles like $3\pi/4$. Look in your book for information about trigonometric functions for angles that are not in the range from $0$ to $\pi/2$. You’ll probably find something very similar to @pjs36’s comment. $\endgroup$ Jul 2, 2015 at 1:52

1 Answer

Step 1: convert angle to degrees

If $\frac{-3\pi}{4}$ is your angle, then you can convert that into degrees by multiplying it with $\frac{360}{2\pi}$ which would get an angle of $-135^o$.

Step 2: Find reference angle

The reference angle here is $45^o$ in the Third Quadrant. This is shown in the picture bellow. I drew that myself (:

Step 3: Determine sign ($+$or$-$) with ASTC (All Students Take Calculus)

The acronym can be seen in the picture above. The acronym is an easy way to remember which trig functions are positive or negative in which quadrants. The letters are assigned to the quadrants in order. ex) A – 1st quad, S- 2nd quad etc.

Step 4: Use special right triangles

We know now that the ref. angle is 45 and only tan is positive (meaning sin and cos are negative). We can then use a 45 45 90 right triangle and SOH CAH TOA to figure out the trig functions.

Using either one of the $45^o$ angles as our reference point, we find that $sin(\frac{-3\pi}{4})=-\frac{1}{\sqrt{2}}$ or $-\frac{\sqrt{2}}{2}$ if you rationalize (also remember there is a negative from ASTC)

Using SOH CAH TOH, you can also find cos and tan (don’t forget cos is – and tan is +). To find sec, csc, and cot, you just need to know that $sec(x)=\frac{1}{cos(x)}$, $csc(x)=\frac{1}{sin(x)}$, and $cot(x)=\frac{1}{tan(x)}$

However, if you are taking Calc, it wouldn’t be a bad idea to memorize all of the trig special angles, since they will appear a lot later

Hope this helps!

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