Question

based on the diagram, pick the two choices below that represent the expression \\(\cos(67)^\circ\\). (note: side lengths are rounded for simplicity, so the expressions may only be approximately equal.)
draw
(diagram of a right triangle with angle 67°, hypotenuse 26, adjacent side 10)
show your work here
hint: to add trig functions, type sin, cos, tan ...
\\(\sin(23)^\circ\\) \\(\sin(67)^\circ\\) \\(\cos(157)^\circ\\) \\(\frac{5}{13}\\) \\(\frac{13}{5}\\)

Explanation:

Step1: Recall cosine in right triangle

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. For $67^\circ$, adjacent side is 10, hypotenuse is 26, so $\cos(67^\circ)=\frac{10}{26}=\frac{5}{13}$.

Step2: Use co - function identity

$\cos(\theta)=\sin(90^\circ - \theta)$. So $\cos(67^\circ)=\sin(90^\circ - 67^\circ)=\sin(23^\circ)$.

Step3: Analyze $\cos(157^\circ)$

$\cos(157^\circ)=\cos(180^\circ - 23^\circ)=-\cos(23^\circ)
eq\cos(67^\circ)$, and $\sin(67^\circ)
eq\cos(67^\circ)$ (since $\sin\theta
eq\cos\theta$ for $\theta = 67^\circ$ generally). Also, $\frac{13}{5}
eq\frac{5}{13}$.

Answer:

The two choices are $\sin(23^\circ)$ and $\frac{5}{13}$