How To Find Sin(5𝜋/6): Using Unit Circle Or Exact Values For Trigonometric Functions

sin 5𝜋/6

sin(5𝜋/6) = -sin(𝜋/6) = -1/2

To find sin(5𝜋/6), we should first note that 5𝜋/6 radians is equal to 150 degrees.

Now, we can use the fact that sin(𝜃) represents the vertical component of a unit circle at an angle of 𝜃.

To visualize this, we can draw a unit circle, which is a circle with a radius of 1, centered at (0,0) on a coordinate plane. Then, for an angle of 150 degrees, we would move clockwise from the positive x-axis.

Using the unit circle, we can see that the vertical component of a point on the circle when we move clockwise from the positive x-axis corresponding to an angle of 150 degrees is -1/2. Therefore, sin(5𝜋/6) = -1/2.

Alternatively, we can use the exact values for trigonometric functions at special angles. In this case, we know that sin(𝜋/6) = 1/2. Using the trigonometric identity sin(𝜋-𝜃) = sin(𝜃), we can rewrite sin(5𝜋/6) as sin(𝜋 – 𝜋/6), which simplifies to sin(5𝜋/6) = -sin(𝜋/6) = -1/2.

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