A point P ( − 11 61 , 60 61 ) P\left(-\frac{11}{61},\frac{60}{61}\right) P ( − 61 11 , 61 60 ) is plotted on the unit circle for a certain angle θ \theta θ . Determine the values of the trigonometric functions sin ⁡ θ \sin\theta sin θ , cos ⁡ θ \cos\theta cos θ , tan ⁡ θ \tan\theta tan θ , cot ⁡ θ \cot\theta cot θ , sec ⁡ θ \sec\theta sec θ , and csc ⁡ θ \csc\theta csc θ corresponding to this point.

sin ⁡ θ = 60 61 \sin\theta=\frac{60}{61} sin θ = 61 60 , cos ⁡ θ = − 11 61 \cos\theta=-\frac{11}{61} cos θ = − 61 11 , tan ⁡ θ = − 60 11 \tan\theta=-\frac{60}{11} tan θ = − 11 60 , cot ⁡ θ = − 11 60 \cot\theta=-\frac{11}{60} cot θ = − 60 11 , sec ⁡ θ = − 61 11 \sec\theta=-\frac{61}{11} sec θ = − 11 61 , csc ⁡ θ = 61 60 \csc\theta=\frac{61}{60} csc θ = 60 61

sin ⁡ θ = − 11 61 \sin\theta=-\frac{11}{61} sin θ = − 61 11 , cos ⁡ θ = 60 61 \cos\theta=\frac{60}{61} cos θ = 61 60 , tan ⁡ θ = − 60 11 \tan\theta=-\frac{60}{11} tan θ = − 11 60 , cot ⁡ θ = − 11 60 \cot\theta=-\frac{11}{60} cot θ = − 60 11 , sec ⁡ θ = − 61 11 \sec\theta=-\frac{61}{11} sec θ = − 11 61 , csc ⁡ θ = 61 60 \csc\theta=\frac{61}{60} csc θ = 60 61

sin ⁡ θ = 60 61 \sin\theta=\frac{60}{61} sin θ = 61 60 , cos ⁡ θ = − 11 61 \cos\theta=-\frac{11}{61} cos θ = − 61 11 , tan ⁡ θ = − 60 11 \tan\theta=-\frac{60}{11} tan θ = − 11 60 , cot ⁡ θ = − 11 60 \cot\theta=-\frac{11}{60} cot θ = − 60 11 , sec ⁡ θ = 61 60 \sec\theta=\frac{61}{60} sec θ = 60 61 , csc ⁡ θ = − 61 11 \csc\theta=-\frac{61}{11} csc θ = − 11 61

sin ⁡ θ = 60 61 \sin\theta=\frac{60}{61} sin θ = 61 60 , cos ⁡ θ = − 11 61 \cos\theta=-\frac{11}{61} cos θ = − 61 11 , tan ⁡ θ = − 11 60 \tan\theta=-\frac{11}{60} tan θ = − 60 11 , cot ⁡ θ = − 60 11 \cot\theta=-\frac{60}{11} cot θ = − 11 60 , sec ⁡ θ = − 61 11 \sec\theta=-\frac{61}{11} sec θ = − 11 61 , csc ⁡ θ = 61 60 \csc\theta=\frac{61}{60} csc θ = 60 61

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0. Review of College Algebra(290)
1. Measuring Angles(322)
2. Trigonometric Functions on Right Triangles(206)
3. Unit Circle(240)
4. Graphing Trigonometric Functions(191)
5. Inverse Trigonometric Functions and Basic Trigonometric Equations(206)
6. Trigonometric Identities and More Equations(341)
7. Non-Right Triangles(117)
8. Vectors(166)
9. Polar Equations(96)
10. Parametric Equations(15)
11. Graphing Complex Numbers(91)

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68PRACTICE PROBLEM

A point $P\left(-\frac{11}{61},\frac{60}{61}\right)$ is plotted on the unit circle for a certain angle $\theta$ . Determine the values of the trigonometric functions $\sin\theta$ , $\cos\theta$ , $\tan\theta$ , $\cot\theta$ , $\sec\theta$ , and $\csc\theta$ corresponding to this point.

ANSWERS OPTIONS

$\sin\theta=-\frac{11}{61}$ , $\cos\theta=\frac{60}{61}$ , $\tan\theta=-\frac{60}{11}$ , $\cot\theta=-\frac{11}{60}$ , $\sec\theta=-\frac{61}{11}$ , $\csc\theta=\frac{61}{60}$

$\sin\theta=\frac{60}{61}$ , $\cos\theta=-\frac{11}{61}$ , $\tan\theta=-\frac{60}{11}$ , $\cot\theta=-\frac{11}{60}$ , $\sec\theta=\frac{61}{60}$ , $\csc\theta=-\frac{61}{11}$

$\sin\theta=\frac{60}{61}$ , $\cos\theta=-\frac{11}{61}$ , $\tan\theta=-\frac{60}{11}$ , $\cot\theta=-\frac{11}{60}$ , $\sec\theta=-\frac{61}{11}$ , $\csc\theta=\frac{61}{60}$

$\sin\theta=\frac{60}{61}$ , $\cos\theta=-\frac{11}{61}$ , $\tan\theta=-\frac{11}{60}$ , $\cot\theta=-\frac{60}{11}$ , $\sec\theta=-\frac{61}{11}$ , $\csc\theta=\frac{61}{60}$

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