How to Find the Value of sin(x) for x = π/3: Unit Circle and Trigonometric Ratios Explained

sinx pi/3

To find the value of sin(x), where x = π/3, we can use the unit circle or the trigonometric ratio values

To find the value of sin(x), where x = π/3, we can use the unit circle or the trigonometric ratio values.

In the unit circle, the angle π/3 corresponds to a point on the circle where the angle subtended from the positive x-axis is π/3. Drawing a line from that point to the origin (0, 0) of the unit circle, we can see that the y-coordinate of that point represents the value of sin(π/3).

In the case of π/3, the point on the unit circle forms an equilateral triangle with two sides of length 1. This means that the y-coordinate of the point is equal to the height of the triangle, which is (√3)/2.

Therefore, sin(π/3) = (√3)/2.

Another way to find the value of sin(π/3) is by referring to the trigonometric ratio values. In this case, sin(π/3) is equivalent to sin(60 degrees) since π/3 is equal to 60 degrees.

The trigonometric ratio values for the commonly used angles (0°, 30°, 45°, 60°, 90°) can be memorized using the acronym “SOH CAH TOA.” In this case, “SOH” represents the sine ratio.

Using the ratio, sin(60°) = (√3)/2, we can conclude that sin(π/3) = (√3)/2 as well.

Therefore, sin(π/3) = (√3)/2.

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