Question

1. express as a function of a different angle, 0° ≤ θ < 360°. tan(196°) tan (____)°

Explanation:

Step1: Identify the quadrant

The angle \(196^\circ\) is in the third quadrant (since \(180^\circ<196^\circ<270^\circ\)). In the third quadrant, the tangent function is positive, and the reference angle is calculated as the angle minus \(180^\circ\).

Step2: Calculate the reference angle

The reference angle \(\theta_{ref}\) for an angle \(\theta\) in the third quadrant is \(\theta - 180^\circ\). So for \(\theta = 196^\circ\), the reference angle is \(196^\circ- 180^\circ=16^\circ\). And we know that \(\tan(\theta)=\tan(\theta - 180^\circ)\) for angles in the third quadrant (because the tangent function has a period of \(180^\circ\) and is positive in the third quadrant). So \(\tan(196^\circ)=\tan(196^\circ - 180^\circ)=\tan(16^\circ)\)

Answer:

\(16\)