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

question 20

Multiple Choice

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

• A) \(\begin{array} { l }
• \tan \theta = - \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = - \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\
• \cot \theta = - \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \csc \theta = - \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } .
• \end{array}\)
• B) \(\begin{array} { l }
• \tan \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sec \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\
• \cot \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \csc \theta = \frac { \sqrt { 10 } } { u } .
• \end{array}\)
• C) \(\begin{array} { l }
• \tan \theta = \frac { \sqrt { 10 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = \frac { \sqrt { 100 - 10 u ^ { 2 } } , } { 10 } , \\
• \cot \theta = \frac { u \sqrt { 10 - u ^ { 2 } } , } { 10 - u ^ { 2 } } , \quad \csc \theta = \frac { \sqrt { 100 - 10 u ^ { 2 } } } { 10 - u ^ { 2 } } .
• \end{array}\)
• D) \(\begin{array} { l }
• \tan \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sec \theta = \frac { \sqrt { 10 } } { u } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\
• \cot \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \csc \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } .
• \end{array}\)
• E) \(\begin{array} { l }
• \tan \theta = \frac { \sqrt { 1 - u ^ { 2 } } } { u } , \quad \sec \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \sin \theta = \frac { \sqrt { 10 - 10 u ^ { 2 } } } { 10 } , \\
• \cot \theta = \frac { u \sqrt { 1 - u ^ { 2 } } } { 1 - u ^ { 2 } } , \quad \csc \theta = \frac { \sqrt { 10 } } { u } .
• \end{array}\)

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