Question

for what angles θ between 0° and 360° is cos θ = sin θ true?
the angle θ in degrees is/are .
(use a comma to separate answers as needed. do not include the degree symbol in your answer.)

Explanation:

Step1: Use trigonometric identity

Given $\cos\theta=\sin\theta$, divide both sides by $\cos\theta$ (assuming $\cos\theta
eq0$), we get $\tan\theta = 1$.

Step2: Recall tangent - angle relationship

We know that $\tan\theta = 1$ when $\theta = 45^{\circ}+180^{\circ}n$, $n\in\mathbb{Z}$.

Step3: Find values in given range

For $n = 0$, $\theta=45$; for $n = 1$, $\theta=45 + 180=225$.

Answer:

45,225