Use the cofunction identities to evaluate the expression below without the aid of a calculator.
$\sin ^ { 2 } 62 ^ { \circ } + \sin ^ { 2 } 30 ^ { \circ } + \sin ^ { 2 } 28 ^ { \circ } + \sin ^ { 2 } 60 ^ { \circ }$
A) 1
B) 2
C) $- 1$
D) 0
E) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

Using the cofunction identities, we know that $\sin(90^\circ - \theta) = \cos(\theta)$ and $\cos(90^\circ - \theta) = \sin(\theta)$. Therefore, $\sin^2(62^\circ) = \cos^2(28^\circ)$ and $\sin^2(28^\circ) = \cos^2(62^\circ)$. Since $\sin^2(\theta) + \cos^2(\theta) = 1$, we can pair $\sin^2(62^\circ) + \sin^2(28^\circ) = 1$ and $\sin^2(30^\circ) + \sin^2(60^\circ) = 1$, because $\sin^2(30^\circ) = 1/4$ and $\sin^2(60^\circ) = 3/4$. Adding these together gives $1 + 1 = 2$.

Use the Cofunction Identities to Evaluate the Expression Below Without sin⁡262∘+sin⁡230∘+sin⁡228∘+sin⁡260∘\sin ^ { 2 } 62 ^ { \circ } + \sin ^ { 2 } 30 ^ { \circ } + \sin ^ { 2 } 28 ^ { \circ } + \sin ^ { 2 } 60 ^ { \circ }sin262∘+sin230∘+sin228∘+sin260∘

Use the Cofunction Identities to Evaluate the Expression Below Without $\sin ^ { 2 } 62 ^ { \circ } + \sin ^ { 2 } 30 ^ { \circ } + \sin ^ { 2 } 28 ^ { \circ } + \sin ^ { 2 } 60 ^ { \circ }$