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Use the Following Information to Express the Remaining Five Trigonometric tt

Question 6

Multiple Choice

Use the following information to express the remaining five trigonometric values as functions of tt . Assume that tt is positive. Rationalize any denominators that contain radicals. cos⁡θ=−3t4,90∘<θ<180∘\cos \theta = - \frac { 3 t } { 4 } , 90 ^ { \circ } < \theta < 180 ^ { \circ }


A) tan⁡θ=−16−9t23t,sec⁡θ=−43t,sin⁡θ=16−9t24,cot⁡θ=−3t16−9t216−9t2,csc⁡θ=416−9t216−9t2.\begin{array} { l } \tan \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = - \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\\cot \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .\end{array}
B) tan⁡θ=−3t16−9t216−9t2,sec⁡θ=−43t,sin⁡θ=16−9t24,cot⁡θ=−16−9t23t,csc⁡θ=416−9t216−9t2.\begin{array} { l } \tan \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \sec \theta = - \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\\cot \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .\end{array}
C) tan⁡θ=16−9t23t,sec⁡θ=43t,sin⁡θ=−16−9t24,cot⁡θ=3t16−9t216−9t2,csc⁡θ=−416−9t216−9t2.\begin{array} { l } \tan \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 } { 3 t } , \quad \sin \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\\cot \theta = \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = - \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .\end{array}
D) tan⁡θ=16−9t23t,sec⁡θ=43t,sin⁡θ=16−9t24,cot⁡θ=3t16−9t216−9t2,csc⁡θ=416−9t216−9t2.\begin{array} { l } \tan \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\\cot \theta = \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .\end{array}
E) tan⁡θ=−16−9t23t,sec⁡θ=416−9t216−9t2,sin⁡θ=16−9t24,cot⁡θ=−3t16−9t216−9t2,csc⁡θ=−43t.\begin{array} { l } \tan \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\\cot \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = - \frac { 4 } { 3 t } .\end{array}

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