Discover the Exact Value of tan 60°: Step-by-Step Guide with Unit Circle and Right Triangle Explanation.

tan 60°

1.732

The exact value of tan 60° is √3 or approximately 1.732.

To explain how we get this value, let’s first look at the unit circle. The unit circle is a circle with its center at the origin (0,0) and radius of 1 unit. The circle intersects the x-axis at (1,0) and (-1,0), and the y-axis at (0,1) and (0,-1).

To find the tangent of an angle, we need to draw a line from the origin to the point on the unit circle that corresponds to that angle. For 60°, we draw a line that makes an angle of 60° with the positive x-axis.

Next, we draw a line perpendicular to the x-axis to form a right triangle. The opposite side is the y-coordinate of the point on the unit circle, which is √3/2. The adjacent side is the x-coordinate, which is 1/2.

Finally, we can use the definition of tangent, which is opposite over adjacent, to find the value of tang 60°.

tan 60° = opposite/adjacent
= (√3/2)/(1/2)
= √3/1
= √3

Therefore, we have found that the value of tan 60° is √3.

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