Question

Let $\theta$ be an angle such that $\cot\theta = -\frac{8}{15}$ and $\sec\theta < 0$. Find the exact values of $\cos\theta$ and $\sin\theta$.

          Let $\theta$ be an angle such that $\cot\theta = -\frac{8}{15}$ and $\sec\theta < 0$.
Find the exact values of $\cos\theta$ and $\sin\theta$.
        
Let θ be an angle such that cotθ = -(8)/(15) and secθ < 0.
Find the exact values of cosθ and sinθ.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Let heta be an angle such that cot heta = -(8)/(15) and sec heta < 0. Find the exact values of cos heta and sin heta. cos heta = sin heta = Let heta be an angle such that cot heta = -(8)/(15) and sec heta < 0. Find the exact values of cos heta and sin heta. cos heta = sin heta =
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Transcript

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00:02 Okay so here cosec theta is equal to 8 by 5 and it is given that cod theta is less than 0 so as we can see that the value of cosec theta is positive but the value of codeta is negative right which means the angle is in second quadrant right okay so as we know sign theta is equal to 1 upon cosec theta right now substitute the value of cosec theta which is 8 divided by 5 so we can write here 5 divided by 8 so this is the value of sine theta now as we know sine square theta plus cos square theta is equal to 1 now substitute the value of sine theta so here sine theta is 5 divided by 8 whole square plus 4 square theta is equal to 1 5 squared that is 25 and 8 square is 64 now subject cos square theta in this equation here 64 multiply by 1 minus 25 that is 39 by 64 now take a square root on both side so here cos theta is equal to square root of 39 upon 64 but here the angle is in second quadrant and in a second quadrant the value of cos theta should be negative right so here negative right now simplify this so here negative square root of 39 and the square root of 64 is 8 right so this is the value of cost theta now as we know 10 theta is equal to sine theta upon cost theta now the sign theta is equal to 5 by 8 and the cost theta that we have already found which is minus 39 upon 8 if your 8 and 8 will be cancelled out so we have only negative 5 upon root 39 right so this is the value of 10 theta right...
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