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Use the Following Information to Express the Remaining Five Trigonometric uu

Question 20

Multiple Choice

Use the following information to express the remaining five trigonometric values as functions of uu . Assume that uu is positive. Rationalize any denominators that contain radicals. cos⁡θ=u10,0∘<θ<90∘\cos \theta = \frac { u } { \sqrt { 10 } } , 0 ^ { \circ } < \theta < 90 ^ { \circ }


A) tan⁡θ=−1−u2u,sec⁡θ=10u,sin⁡θ=−10−10u210,cot⁡θ=−u1−u21−u2,csc⁡θ=−10−10u21−u2.\begin{array} { l } \tan \theta = - \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = - \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\\cot \theta = - \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \csc \theta = - \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } .\end{array}
B) tan⁡θ=u1−u21−u2,sec⁡θ=10−10u21−u2,sin⁡θ=10−10u210,cot⁡θ=1−u2u,csc⁡θ=10u.\begin{array} { l } \tan \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sec \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\\cot \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \csc \theta = \frac { \sqrt { 10 } } { u } .\end{array}
C) tan⁡θ=10−u2u,sec⁡θ=10u,sin⁡θ=100−10u2,10,cot⁡θ=u10−u2,10−u2,csc⁡θ=100−10u210−u2.\begin{array} { l } \tan \theta = \frac { \sqrt { 10 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = \frac { \sqrt { 100 - 10 u ^ { 2 } } , } { 10 } , \\\cot \theta = \frac { u \sqrt { 10 - u ^ { 2 } } , } { 10 - u ^ { 2 } } , \quad \csc \theta = \frac { \sqrt { 100 - 10 u ^ { 2 } } } { 10 - u ^ { 2 } } .\end{array}
D) tan⁡θ=u1−u21−u2,sec⁡θ=10u,sin⁡θ=10−10u210,cot⁡θ=1−u2u,csc⁡θ=10−10u21−u2.\begin{array} { l } \tan \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\\cot \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \csc \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } .\end{array}
E) tan⁡θ=1−u2u,sec⁡θ=10−10u21−u2,sin⁡θ=10−10u210,cot⁡θ=u1−u21−u2,csc⁡θ=10u.\begin{array} { l } \tan \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\\cot \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \csc \theta = \frac { \sqrt { 10 } } { u } .\end{array}

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