Question

the terminal ray of an angle θ intersects the unit circle as shown below. use the given coordinates to calculate tan θ rounded to three decimal places, if necessary. (-0.574,0.819) answer attempt 1 out of 3 tan θ = submit answer

Explanation:

Step1: Recall the definition of tangent on the unit circle

For a point \((x, y)\) on the unit circle, \(\tan\theta=\frac{y}{x}\). Here, the coordinates of the point are \((-0.574, 0.819)\), so \(x = - 0.574\) and \(y=0.819\).

Step2: Calculate \(\tan\theta\)

Substitute \(x\) and \(y\) into the formula: \(\tan\theta=\frac{0.819}{-0.574}\)
Calculate the value: \(\frac{0.819}{-0.574}\approx - 1.427\)

Answer:

\(-1.427\)