Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
$\cos \beta = \frac { \sqrt { 5 } } { 4 }$ $\sec \beta \text { and } \sin \left( 90 ^ { \circ } - \beta \right)$
A) $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
B) $\sec \beta = \sqrt { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = 4$
C) $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
D) $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$
E) $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$

Question

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. 
 $\cos \beta = \frac { \sqrt { 5 } } { 4 }$   $\sec \beta \text { and } \sin \left( 90 ^ { \circ } - \beta \right)$  
A) $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
B)  $\sec \beta = \sqrt { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = 4$
C)  $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
D)  $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$
E)  $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$

Quizplus · Accepted Answer

$\sec \beta = \frac{1}{\cos \beta} = \frac{1}{\sqrt{5}/4} = \frac{4}{\sqrt{5}} = \frac{4\sqrt{5}}{5}$. $\sin(90^\circ - \beta) = \cos \beta = \frac{\sqrt{5}}{4}$ due to cofunction identity.

Use the Given Function Value(s), and Trigonometric Identities (Including the Cofunction