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Find all angles,
0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree.

tan^(2)theta-tan theta=0
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree. $\newline$ $\tan ^{2} \theta-\tan \theta=0$ $\newline$ Answer: $\theta=$

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Find roots using a calculator

Full solution

Q. Find all angles,

0^{\circ} \leq \theta<360^{\circ}

, that satisfy the equation below, to the nearest tenth of a degree.

\newline

\tan ^{2} \theta-\tan \theta=0

\newline

Answer:

\theta=

Factor and Solve: We are given the equation $\tan^2\theta - \tan \theta = 0$ . To solve for $\theta$ , we first factor the left side of the equation. $\newline$ $\tan \theta * (\tan \theta - 1) = 0$ $\newline$ This gives us two separate equations to solve: $\newline$ $1$ ) $\tan \theta = 0$ $\newline$ $2$ ) $\tan \theta - 1 = 0$
Solve $\tan \theta = 0$ : Let's solve the first equation $\tan \theta = 0$ . The tangent of an angle is zero at $0$ degrees and $180$ degrees within the range of $0$ to $360$ degrees. So, $\theta = 0$ degrees and $\theta = 180$ degrees.
Solve $\tan \theta - 1 = 0$ : Now, let's solve the second equation $\tan \theta - 1 = 0$ . This simplifies to $\tan \theta = 1$ . The tangent of an angle is equal to $1$ at $45$ degrees and $225$ degrees within the range of $0$ to $360$ degrees. So, $\theta = 45$ degrees and $\theta = 225$ degrees.
Final Angles: We have found all the angles that satisfy the given equation: $\theta = 0$ degrees, $\theta = 45$ degrees, $\theta = 180$ degrees, and $\theta = 225$ degrees. These are the angles to the nearest tenth of a degree.

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