The terminal side of an angle θ in standard position intersects the unit circle at 3989,8089. What is tan(θ)?
Question
The terminal side of an angle θ in standard position intersects the unit circle at 3989,8089. What is tan(θ)?
Solution
The point on the unit circle is given as (3989, 8089).
In the unit circle, the x-coordinate represents the cosine of the angle (cos θ) and the y-coordinate represents the sine of the angle (sin θ).
The tangent of the angle (tan θ) is given by the ratio of the sine to the cosine, or in this case, the y-coordinate to the x-coordinate.
So, tan(θ) = sin(θ) / cos(θ) = 8089 / 3989.
Therefore, tan(θ) = 8089 / 3989.
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