Question

a triangle is graphed on the unit circle as shown.
what is the value of tan(θ) for the triangle where θ is the labeled angle? round decimal answers to the nearest hundredth.
a. 1.73
b. -0.58
c. 0.58
d. -1.73

Explanation:

Step1: Recall the formula for tangent

The formula for tangent in a right - triangle is \(\tan\theta=\frac{y}{x}\).

Step2: Identify the \(x\) and \(y\) values

From the point \((-\frac{1}{2},\frac{\sqrt{3}}{2})\), we have \(x =-\frac{1}{2}\) and \(y=\frac{\sqrt{3}}{2}\).

Step3: Calculate \(\tan\theta\)

Substitute \(x\) and \(y\) into the formula: \(\tan\theta=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}\).

Step4: Approximate \(-\sqrt{3}\)

Since \(\sqrt{3}\approx1.73\), then \(-\sqrt{3}\approx - 1.73\).

Answer:

D. -1.73