Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. 4cos^(2)theta+17 cos theta+7=5cos theta+2 Answer: theta=

Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation to zero. 4cos²(theta) + 17cos(theta) + 7 = 5cos(theta) + 2 4cos²(theta) + 17cos(theta) + 7 - 5cos(theta) - 2 = 0 4cos²(theta) + 12cos(theta) + 5 = 0Factor Quadratic: Factor the quadratic equation in terms of cos(theta). We are looking for factors of 4cos²(theta) and 5 that add up to 12cos(theta). (4cos(theta) + 5)(cos(theta) + 1) = 0Solve First Factor: Solve each factor for cos(theta). First factor: 4cos(theta) + 5 = 0 cos(theta) = -5/4 Since the cosine of an angle cannot be less than -1 or greater than 1, this solution is not possible.Solve Second Factor: Solve the second factor for cos(theta). Second factor: cos(theta) + 1 = 0 cos(theta) = -1Find Angle: Find the angles theta that correspond to cos(theta) = -1. The cosine of an angle is equal to -1 at theta = 180 degrees.Check Range: Check the range for theta. Since we are looking for angles between 0 degrees and 360 degrees, the only angle that satisfies the equation and is within the range is theta = 180 degrees.

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

4cos^(2)theta+17 cos theta+7=5cos theta+2
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree. $\newline$ $4 \cos ^{2} \theta+17 \cos \theta+7=5 \cos \theta+2$ $\newline$ Answer: $\theta=$

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Algebra 2

Csc, sec, and cot of special angles

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Q. Find all angles,

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

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

\newline

4 \cos ^{2} \theta+17 \cos \theta+7=5 \cos \theta+2

\newline

Answer:

\theta=

Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation to zero. $\newline$ $4\cos^2(\theta) + 17\cos(\theta) + 7 = 5\cos(\theta) + 2$ $\newline$ $4\cos^2(\theta) + 17\cos(\theta) + 7 - 5\cos(\theta) - 2 = 0$ $\newline$ $4\cos^2(\theta) + 12\cos(\theta) + 5 = 0$
Factor Quadratic: Factor the quadratic equation in terms of $\cos(\theta)$ . We are looking for factors of $4\cos^2(\theta)$ and $5$ that add up to $12\cos(\theta)$ . $(4\cos(\theta) + 5)(\cos(\theta) + 1) = 0$
Solve First Factor: Solve each factor for $\cos(\theta)$ . $\newline$ First factor: $4\cos(\theta) + 5 = 0$ $\newline$ $\cos(\theta) = -\frac{5}{4}$ $\newline$ Since the cosine of an angle cannot be less than $-1$ or greater than $1$ , this solution is not possible.
Solve Second Factor: Solve the second factor for $\cos(\theta)$ . $\newline$ Second factor: $\cos(\theta) + 1 = 0$ $\newline$ $\cos(\theta) = -1$
Find Angle: Find the angles $\theta$ that correspond to $\cos(\theta) = -1$ . The cosine of an angle is equal to $-1$ at $\theta = 180$ degrees.
Check Range: Check the range for $\theta$ . $\newline$ Since we are looking for angles between $0$ degrees and $360$ degrees, the only angle that satisfies the equation and is within the range is $\theta = 180$ degrees.