How do you evaluate #sin(pi/3) #?

Answer 1
For trigonometry, it is imperative to memorize a tool known as the Unit Circle. This is a circle with a radius of #1# and a center on the origin. The points on the circumference of the circle are the coordinates that you need to know.
When you see a trigonometric function such as sine (or sin(#theta#)) or cosine (or cos(#theta#)), it refers the point on the circumference of the circle that intersects the line coming from the origin at a given angle (#theta#) counter-clockwise from the axis between Quadrant I and Quadrant IV of the coordinate plane.
In this case, #pi/3# refers to the angle in radians, an alternate unit of measurement for angles (#pi# rad = 180°) that is generally used in trigonometry. The point on the unit circle that is intersected by this line is (#1/2#, #sqrt(3)/2#). Finally, the function, sin(#theta#) returns a value equal to the y-coordinate of the point, giving us an answer of #sqrt(3)/2#.

In the future, you should memorize all the major points on the unit circle along with their reference angles and you'll be able to find these answers quickly.

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Answer 2

To evaluate (\sin(\frac{\pi}{3})), you can use the trigonometric values for common angles. In this case, (\frac{\pi}{3}) corresponds to a (60^\circ) angle.

The exact value of (\sin(\frac{\pi}{3})) is (\frac{\sqrt{3}}{2}). This value is commonly memorized or derived from the properties of special right triangles, such as the (30^\circ)-(60^\circ)-(90^\circ) triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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