Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. 4tan^(2)theta+3tan theta-1=3tan theta Answer: theta=

Simplify Equation: Simplify the given equation by subtracting 3tan(theta) from both sides. 4tan^2(theta) + 3tan(theta) - 1 = 3tan(theta) 4tan^2(theta) + 3tan(theta) - 3tan(theta) - 1 = 0 4tan^2(theta) - 1 = 0Solve Quadratic Equation: Solve the simplified quadratic equation for tan(theta). 4tan^2(theta) - 1 = 0 (2tan(theta) - 1)(2tan(theta) + 1) = 0Set and Solve Factors: Set each factor equal to zero and solve for tan(theta). 2tan(theta) - 1 = 0 or 2tan(theta) + 1 = 0 tan(theta) = 1/2 or tan(theta) = -1/2Find Corresponding Angles: Find the angles theta that correspond to tan(theta) = 1/2 and tan(theta) = -1/2 within the range 0 degrees <= theta < 360 degrees. For tan(theta) = 1/2, the angles are approximately 26.6 degrees and 206.6 degrees. For tan(theta) = -1/2, the angles are approximately 333.4 degrees and 153.4 degrees.

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

4tan^(2)theta+3tan theta-1=3tan theta
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree. $\newline$ $4 \tan ^{2} \theta+3 \tan \theta-1=3 \tan \theta$ $\newline$ 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 \tan ^{2} \theta+3 \tan \theta-1=3 \tan \theta

\newline

Answer:

\theta=

Simplify Equation: Simplify the given equation by subtracting $3\tan(\theta)$ from both sides. $\newline$ $4\tan^2(\theta) + 3\tan(\theta) - 1 = 3\tan(\theta)$ $\newline$ $4\tan^2(\theta) + 3\tan(\theta) - 3\tan(\theta) - 1 = 0$ $\newline$ $4\tan^2(\theta) - 1 = 0$
Solve Quadratic Equation: Solve the simplified quadratic equation for $\tan(\theta)$ . $4\tan^2(\theta) - 1 = 0$ $(2\tan(\theta) - 1)(2\tan(\theta) + 1) = 0$
Set and Solve Factors: Set each factor equal to zero and solve for $\tan(\theta)$ . $2\tan(\theta) - 1 = 0$ or $2\tan(\theta) + 1 = 0$ $\tan(\theta) = \frac{1}{2}$ or $\tan(\theta) = -\frac{1}{2}$
Find Corresponding Angles: Find the angles $\theta$ that correspond to $\tan(\theta) = \frac{1}{2}$ and $\tan(\theta) = -\frac{1}{2}$ within the range 0^\circ \leq \theta < 360^\circ. For $\tan(\theta) = \frac{1}{2}$ , the angles are approximately $26.6^\circ$ and $206.6^\circ$ . For $\tan(\theta) = -\frac{1}{2}$ , the angles are approximately $333.4^\circ$ and $153.4^\circ$ .