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Determine $\sin(\theta) + \cos(\theta)$ if $\csc(\theta) = 3$ and $\theta$ is in Quadrant II. Leave your answer in exact form.

I am unsure of where to begin with this problem. I cannot use a calculator a step by step to help me learn this type would be appreciated.

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  • $\begingroup$ If $\csc \theta = 3$ and $\theta$ is in Quadrant II, you have enough data to draw an accurate diagram of the angle in question. Just recall the basic definition of $\csc$. Then, $\sin \theta$ can be solved easily from $\csc \theta$, and the Pythagorean Theorem will let you solve for the third side of the triangle, allowing you to calculate $\cos \theta$. $\endgroup$ – Wildcard Oct 12 '15 at 21:35
  • $\begingroup$ How is $\csc\theta$ related to $\sin\theta$? How do you determine the value of $\cos\theta$ if you know the value of $\sin\theta$? $\endgroup$ – N. F. Taussig Oct 12 '15 at 21:35
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Draw a triangle. Opposite side is 1, hypotenuse is 3, adjacent side is $ 2 \sqrt2$ Find sin,cos.Note the signs $+,-$ respectively.

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