Question

1. -/2 points find the reference angle θ. (round your answer to four decimal places.) θ = 4.9 θ = rad sketch θ and θ in standard position.

Explanation:

Step1: Determine the quadrant

Since \(2\pi\approx6.28\) and \(\pi\approx3.14\), and \(\pi<4.9 < 2\pi\), the angle \(\theta = 4.9\) radians is in the fourth - quadrant.

Step2: Calculate the reference angle

The formula for the reference angle \(\theta'\) of an angle \(\theta\) in the fourth - quadrant is \(\theta'=2\pi-\theta\). Substitute \(\theta = 4.9\) into the formula: \(\theta'=2\pi - 4.9\). Using \(\pi\approx3.14159\), we have \(\theta'=2\times3.14159 - 4.9=6.28318-4.9 = 1.3832\).

Answer:

\(1.3832\)