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: Rewrite the equation

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

Step2: Find the principal - value solution

We know that $\tan\theta = 1$ has a principal - value solution $\theta=\arctan(1)$. In the range of $0^{\circ}$ to $360^{\circ}$, the tangent function $y = \tan\theta$ has a period of $180^{\circ}$. The principal - value of $\theta$ for which $\tan\theta=1$ is $\theta = 45^{\circ}$.

Step3: Find all solutions in the given range

Since the period of the tangent function is $180^{\circ}$, we find other solutions in the range $0^{\circ}\leq\theta<360^{\circ}$ by adding $180^{\circ}$ to the principal - value. So $\theta=45^{\circ}+180^{\circ}=225^{\circ}$.

Answer:

45,225