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EDIT: IM DONE WITH THIS PROBLEM, THANKS FOR THE HELP

Evaluate the expression under the given conditions.

My work (got lost and don't know what to do from here):

EDIT: Sin theta should be -3/5

Can someone explain to me how I'm supposed to solve this? I was absent at school today and this is one of the homework questions.

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  • $\begingroup$ There are several issues. Firstly, $\theta$ is not -3/4, and $\phi$ is not what you wrote So the very first step is incorrect. $\endgroup$ – Shailesh Jul 31 '15 at 2:39
  • $\begingroup$ whoops theta is -3/5, and isn't ϕ correct since it is given in the question above? $\endgroup$ – TheNewGuy Jul 31 '15 at 2:43
  • $\begingroup$ Those are not the values of the angles. They are the values of sin, cos or tan as the case may be $\endgroup$ – Shailesh Jul 31 '15 at 2:48
  • $\begingroup$ Would I take the inverse to get the angles? $\endgroup$ – TheNewGuy Jul 31 '15 at 2:57
  • $\begingroup$ I think you are looking at the equation "$\tan\theta=\frac34$" and seeing it grouped as "$(\tan)(\theta=\frac34)$" instead of "$(\tan\theta)=(\frac34)$". The first is meaningless. "$\tan$" is a function and you should think of "$\tan\theta$" like "$f(x)$". We usually leave off the parentheses for trig functions unless needed to prevent confusion, so you will usually see things like "$\sin 3x$" instead of "$\sin(3x)$". $\endgroup$ – MPW Jul 31 '15 at 3:01
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HINTS:

If $\tan \theta =\frac34$ and $\theta$ is "in the third quadrant" implies that $\sin \theta =-3/5$ and $\cos \theta =-4/5$.

If $\sin \phi =-\sqrt{10}/10$ and $\phi$ is "in the fourth quadrant", then $\cos \phi=3\sqrt{10}/10$.

Can you finish from here?

SPOILER ALERT: SCROLL OVER SHADED AREA TO SEE SOLUTION

\begin{align}\sin (\theta -\phi)&=\sin \theta\,\cos \phi-\sin \phi\,\cos \theta\\\\&=-\frac35\,\frac{3\sqrt{10}}{10}+\frac45\,\frac{\sqrt{10}}{10}\\\\&=-\frac{\sqrt{10}}{10}\end{align}

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  • $\begingroup$ Please let me know how I can improve my answer. I really want to help and give you the best answer I can. $\endgroup$ – Mark Viola Aug 10 '15 at 2:36

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