Question

The line connecting the origin to the circumference of the quarter circle meets the circumference of the circle at left parenthesis Start Fraction Start Root 3 End Root over 2 End Fraction comma Start Fraction 1 over 2 End Fraction right parenthesis. The sides of the right triangle are labeled as follows: the base is given as Start Fraction Start Root 3 End Root over 2 End Fraction, the side perpendicular to the base which connects with the circumference point is given as Start Fraction 1 over 2 End Fraction, and the hypotenuse of the right triangle is given as 1. A square is drawn in the interior angle between the base of the right triangle and the side perpendicular to the base. The interior angle between the base and the hypotenuse is labeled as theta.

Use the triangle shown on the unit circle to find tanθ
.

(1 point)
Responses

1
1

3–√

Start Root 3 End Root

3√3

Start Fraction Start Root 3 End Root over 3 End Fraction

3√4

Start Fraction Start Root 3 End Root over 4 End Fraction
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Answer 1

tanθ = (1/2) / (√3/2) = 1/√3 = √3/3.