Find all angles, 0^(@) <= theta < 360^(@), that solve the following equation. tan theta=sqrt3 Answer: theta=

Recognize Equation: Recognize that the equation tan(theta) = sqrt(3) is looking for angles where the tangent function has the value of sqrt(3). The tangent function has the value of sqrt(3) at angles where the opposite side over the adjacent side of a right triangle equals sqrt(3), which corresponds to an equilateral triangle cut in half, forming a 30-60-90 triangle. Therefore, the reference angle for which tan(theta) = sqrt(3) is 60 degrees.Find Reference Angle: Determine the angles in the interval [0, 360) degrees where the tangent function is positive. Tangent is positive in the first and third quadrants. Since the reference angle is 60 degrees, the angles that satisfy the equation in these quadrants are 60 degrees and 180 + 60 = 240 degrees.Determine Positive Quadrants: Write down the final answer with the angles found in Step 2. The angles that satisfy the equation tan(theta) = sqrt(3) in the interval [0, 360) degrees are 60 degrees and 240 degrees.

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Find all angles,
0^(@) <= theta < 360^(@), that solve the following equation.

tan theta=sqrt3
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation. $\newline$ $\tan \theta=\sqrt{3}$ $\newline$ Answer: $\theta=$

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Find all angles,

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

, that solve the following equation.

\newline

\tan \theta=\sqrt{3}

\newline

Answer:

\theta=

Recognize Equation: Recognize that the equation $\tan(\theta) = \sqrt{3}$ is looking for angles where the tangent function has the value of $\sqrt{3}$ . The tangent function has the value of $\sqrt{3}$ at angles where the opposite side over the adjacent side of a right triangle equals $\sqrt{3}$ , which corresponds to an equilateral triangle cut in half, forming a $30$ - $60$ - $90$ triangle. Therefore, the reference angle for which $\tan(\theta) = \sqrt{3}$ is $60$ degrees.
Find Reference Angle: Determine the angles in the interval $[0, 360)$ degrees where the tangent function is positive. $\newline$ Tangent is positive in the first and third quadrants. Since the reference angle is $60$ degrees, the angles that satisfy the equation in these quadrants are $60$ degrees and $180 + 60 = 240$ degrees.
Determine Positive Quadrants: Write down the final answer with the angles found in Step $2$ . $\newline$ The angles that satisfy the equation $\tan(\theta) = \sqrt{3}$ in the interval $[0, 360)$ degrees are $60$ degrees and $240$ degrees.