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

cos^(2)theta-cos 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. $\newline$ $\cos ^{2} \theta-\cos \theta=0$ $\newline$ Answer: $\theta=$

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Find the roots of factored polynomials

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

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

\newline

Answer:

\theta=

Identify Trigonometric Equation: First, let's identify the trigonometric equation we need to solve: $\cos^2(\theta) - \cos(\theta) = 0$ . We can factor this equation to find the values of $\theta$ that satisfy it. Factor out $\cos(\theta)$ : $\cos(\theta)(\cos(\theta) - 1) = 0$ . Now we have two factors that can be individually set to zero to find the solutions for $\theta$ .
Factor and Solve: Set the first factor equal to zero: $\cos(\theta) = 0$ . To find the angles where the cosine of $\theta$ is zero, we look at the unit circle. Cosine is zero at $90$ degrees ( $\pi/2$ radians) and $270$ degrees ( $3\pi/2$ radians).
Find Cosine Values: Set the second factor equal to zero: $\cos(\theta) - 1 = 0$ . Solve for $\cos(\theta)$ : $\cos(\theta) = 1$ . The angle where the cosine of $\theta$ is one is at $0$ degrees ( $0$ radians).
Solve for Theta: Now we have all the angles that satisfy the equation within the range of $0$ to $360$ degrees. $\newline$ The angles are $0$ degrees, $90$ degrees, and $270$ degrees. $\newline$ Convert these angles to the nearest tenth of a degree, which in this case does not change the values since they are already whole numbers.

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