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I'm having issues understanding as to how to go about doing this. I cant seem to figure out how to find the values of sin and tan in terms of the given cos value in the 3rd quadrant. Thanks with any and all help.

$\cos[\theta] = \frac{-4}{5}$ and theta is in the 3rd quadrant, find the exact values of (i) $\sin[\theta]$ (ii) $\tan[\theta]$

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  • $\begingroup$ Well, what do you know about the sign of the sine and tangent functions when the angle is in the third quadrant? If you use this and Pythagoras' Theorem, you should be able to get the answer. $\endgroup$ – dodo628 Aug 22 '15 at 2:33
  • $\begingroup$ Recall that $cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ $\endgroup$ – Paddling Ghost Aug 22 '15 at 2:33
  • $\begingroup$ Remember that $\cos\theta$ is just the $x$-coordinate of a point at angle $\theta$ on the unit circle. Knowing that $\cos\theta = -\frac45$ and that $\theta$ is in the third quadrant, you should be able to make a rough sketch of that point. $\endgroup$ – David K Aug 22 '15 at 2:43
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This is a table that expresses sin, cos and tan in terms of each other.

Converting trigonometric functions to others.

You don't need to remember the table... just substitute values in the triangle, find the third side using Pythagoras and find the value of the required function.

Right angled triangle

Also, you just need to remember which trigonometric function is positive in which quadrant using this table.

Quadrant signs

This can be remembered using the simple mnemonic.. After School To College.

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  • $\begingroup$ All Students Take Calculus... Just because mnemonics are everything. $\endgroup$ – user134593 Aug 22 '15 at 2:49
  • $\begingroup$ Or A Smart Trig Class, or All Stores Take Cash, or Aunt Sally Tickles Cobras.. :D $\endgroup$ – RedDragon Aug 22 '15 at 3:00
  • $\begingroup$ All good mnemonics! Haha I use them for everything memorizable. $\endgroup$ – user134593 Aug 22 '15 at 3:29

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