Question

which of the following expressions has the same value as $cos 30^circ$? (1 point) $\bigcirc sin 30^circ$ $\bigcirc cos 60^circ$ $\bigcirc sin \frac{pi}{6}$ $\bigcirc cos \frac{pi}{6}$

Explanation:

Step1: Recall trigonometric values

We know the following trigonometric values:

• $\cos 30^{\circ}=\frac{\sqrt{3}}{2}$
• $\sin 30^{\circ}=\frac{1}{2}$
• $\cos 60^{\circ}=\frac{1}{2}$
• $\sin\frac{\pi}{6}=\sin 30^{\circ}=\frac{1}{2}$ (since $\frac{\pi}{6}$ radians is $30^{\circ}$)
• $\cos\frac{\pi}{6}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}$ (since $\frac{\pi}{6}$ radians is $30^{\circ}$)

Step2: Compare values

Now we compare the value of $\cos 30^{\circ}$ with each option:

• $\sin 30^{\circ}=\frac{1}{2}

eq\frac{\sqrt{3}}{2}$

• $\cos 60^{\circ}=\frac{1}{2}

eq\frac{\sqrt{3}}{2}$

• $\sin\frac{\pi}{6}=\frac{1}{2}

eq\frac{\sqrt{3}}{2}$

• $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}=\cos 30^{\circ}$

Answer:

$\cos \frac{\pi}{6}$ (the last option, which is $\boldsymbol{\cos \frac{\pi}{6}}$)