Question

for what angles are sine and cosine the same? 0° 45° and 225° 45° and 135° 45° and 315°

Explanation:

Step1: Recall the trigonometric identity

We know that \(\sin\theta=\cos\theta\). Dividing both sides by \(\cos\theta\) (assuming \(\cos\theta
eq0\)), we get \(\tan\theta = 1\).

Step2: Find the general solution for \(\tan\theta=1\)

The general solution for \(\tan\theta = 1\) is \(\theta=n\times180^{\circ}+45^{\circ}\), where \(n\in\mathbb{Z}\).

Step3: Find the solutions in the range of \(0^{\circ}\leq\theta < 360^{\circ}\)

When \(n = 0\), \(\theta=45^{\circ}\); when \(n = 1\), \(\theta=180^{\circ}+45^{\circ}=225^{\circ}\)

Answer:

\(45^{\circ}\) and \(225^{\circ}\)