Question

Let $\theta$ be an angle in quadrant III such that $\sec \theta = -\frac{9}{4}$. Find the exact values of $\cot \theta$ and $\sin \theta$.

          Let $\theta$ be an angle in quadrant III such that $\sec \theta = -\frac{9}{4}$.

Find the exact values of $\cot \theta$ and $\sin \theta$.
        
Let θ be an angle in quadrant III such that secθ = -(9)/(4).

Find the exact values of cotθ and sinθ.

Added by Andrew M.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Let heta be an angle in quadrant III such that sec heta =-(9)/(4). Find the exact values of cot heta and sin heta . 9 Let 0 be an angle in quadrant III such that sec 0= Find the exact values of cot 0 and sin 0.
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Transcript

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00:01 Okay, so we're given in this problem that cosine of theta is equal to just double checking negative 4 -fiths.
00:10 And we also know that we're in quadrant three, so let me just draw that real quick.
00:13 If you're in quadrant three, what i like to do is make the angle made with the x -axis.
00:20 So it's right here.
00:22 And cosine is adjacent over hypotenuse.
00:25 So this side will be negative four.
00:27 This side would be five.
00:27 And this is a 3, 4, 5 right triangle.
00:32 You might even call it a pythagorean triple because it's always true that 3 squared plus 4 squared equals 5 squared.
00:39 So i would encourage you to memorize that...
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