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

Quizplus · Accepted Answer

Using the given function value of sine, we can determine the cosine using the cofunction identity:
cos(θ) = sin(90° - θ)
cos(30°) = sin(90° - 30°) = sin(60°) = √3/2

Using the given function value of tangent, we can determine the adjacent and hypotenuse using the Pythagorean identity:
tan(θ) = sin(θ) / cos(θ)
tan(45°) = sin(45°) / cos(45°) 
1 = sin(45°) / cos(45°)
cos(45°) = sin(45°) = 1/√2
Using the adjacent and hypotenuse, we can determine the sine using the Sokotoa identity:
sin(θ) = opposite / hypotenuse
sin(45°) = 1/√2 / √2 = 1/2

Use the Given Function Value(s),and Trigonometric Identities (Including the Cofunction cos⁡β=54\cos \beta = \frac { \sqrt { 5 } } { 4 }cosβ=45​​

Use the Given Function Value(s),and Trigonometric Identities (Including the Cofunction $\cos \beta = \frac { \sqrt { 5 } } { 4 }$