Use the Following Information to Express the Remaining Five Trigonometric $t$

question 6

Multiple Choice

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

• A) \(\begin{array} { l }
• \tan \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = - \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\
• \cot \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .
• \end{array}\)
• B) \(\begin{array} { l }
• \tan \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \sec \theta = - \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\
• \cot \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .
• \end{array}\)
• C) \[\begin{array} { l }
• \tan \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 } { 3 t } , \quad \sin \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\
• \cot \theta = \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = - \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .
• \end{array}\]
• D) \(\begin{array} { l }
• \tan \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 } { 3 t } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\
• \cot \theta = \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } .
• \end{array}\)
• E) \(\begin{array} { l }
• \tan \theta = - \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 3 t } , \quad \sec \theta = \frac { 4 \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 16 - 9 t ^ { 2 } } } { 4 } , \\
• \cot \theta = - \frac { 3 t \sqrt { 16 - 9 t ^ { 2 } } } { 16 - 9 t ^ { 2 } } , \quad \csc \theta = - \frac { 4 } { 3 t } .
• \end{array}\)

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