What is $\sin 60^{\circ}$?
A. $\frac{1}{2}$
B. $\frac{\sqrt{3}}{2}$
C. $\sqrt{3}$
D. 1
E. $\frac{1}{\sqrt{2}}$
F. $\frac{1}{\sqrt{3}}$
Answer (1)
The problem requires finding the value of sin 6 0 ∘ .
Recall the standard trigonometric values.
State that sin 6 0 ∘ = 2 3 .
The correct answer is 2 3 .
Explanation
Problem Analysis The problem asks us to find the value of sin 6 0 ∘ . We need to recall the standard trigonometric values for common angles.
Recall Trigonometric Values We know that sin 6 0 ∘ is a standard trigonometric value that is commonly memorized.
State the Value The value of sin 6 0 ∘ is 2 3 .
Identify the Correct Option Comparing this to the given options, we see that option B, 2 3 , is the correct answer.
Examples
Understanding trigonometric values like sin 6 0 ∘ is crucial in various fields. For instance, in physics, when analyzing projectile motion, you need to calculate the vertical component of the initial velocity, which often involves trigonometric functions. If a ball is thrown at an initial velocity v at an angle of 6 0 ∘ with the horizontal, the vertical component of the velocity is v sin 6 0 ∘ = v 2 3 . Similarly, in engineering, when designing structures, you need to calculate forces acting at angles, which also involves trigonometric functions. Knowing these values helps in quick and accurate calculations.
