What is [tex]$\sin 60^{\circ}$[/tex]?
A. [tex]$\frac{1}{2}$[/tex]
B. [tex]$\sqrt{3}$[/tex]
C. [tex]$\frac{1}{\sqrt{2}}$[/tex]
D. [tex]$\frac{\sqrt{3}}{2}$[/tex]
E. 1
F. [tex]$\frac{1}{\sqrt{3}}$[/tex]
Answer (2)
The value of sin 6 0 ∘ is 2 3 , derived from the properties of a 30-60-90 triangle. This value is well-known in trigonometry and corresponds to option D. Therefore, the chosen option is D: 2 3 .
;
Recall the standard trigonometric values.
Identify that sin 6 0 ∘ = 2 3 .
Match the value with the given options.
The 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, such as 30°, 45°, and 60°.
Recall Trigonometric Values We know that sin 6 0 ∘ is a standard trigonometric value that should be memorized or easily derived from the unit circle or a 30-60-90 triangle.
State the Value The value of sin 6 0 ∘ is 2 3 .
Identify the Correct Option Comparing this value with the given options, we find that option D, 2 3 , is the correct answer.
Examples
Understanding trigonometric values like sin 6 0 ∘ is crucial in many real-world applications. For example, when designing a roof, knowing the angle of the roof and the length of one side allows you to calculate the length of the other sides using trigonometric functions. Similarly, in physics, when analyzing projectile motion, the initial velocity can be broken down into horizontal and vertical components using sine and cosine functions. Knowing these values helps engineers and scientists make accurate predictions and designs.
