Find all angles, 0^(@) <= theta < 360^(@), that solve the following equation. sin theta=(sqrt3)/(2) Answer: theta=

Recognize Standard Angle: Recognize that sin theta = sqrt(3)/2 corresponds to the standard angle of 60° in the unit circle. However, since the sine function is positive in both the first and second quadrants, we need to find the angles in both quadrants that have this sine value.First Quadrant Solution: The angle in the first quadrant that has a sine value of sqrt(3)/2 is 60°. This is one of the solutions.Second Quadrant Solution: To find the angle in the second quadrant, we use the fact that sine is symmetric about 180°. The second quadrant angle will be 180° - 60° = 120°. This is the second solution.Check for Other Solutions: Check for any other angles within the range 0° <= theta < 360° that might have the same sine value. Since the sine function repeats every 360°, and the problem only asks for angles within one full rotation, there are no more solutions.

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

sin theta=(sqrt3)/(2)
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation. $\newline$ $\sin \theta=\frac{\sqrt{3}}{2}$ $\newline$ Answer: $\theta=$

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Math Problems

Algebra 2

Csc, sec, and cot of special angles

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Q. Find all angles,

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

, that solve the following equation.

\newline

\sin \theta=\frac{\sqrt{3}}{2}

\newline

Answer:

\theta=

Recognize Standard Angle: Recognize that $\sin \theta = \sqrt{3}/2$ corresponds to the standard angle of $60^\circ$ in the unit circle. However, since the sine function is positive in both the first and second quadrants, we need to find the angles in both quadrants that have this sine value.
First Quadrant Solution: The angle in the first quadrant that has a sine value of $\sqrt{3}/2$ is $60^\circ$ . This is one of the solutions.
Second Quadrant Solution: To find the angle in the second quadrant, we use the fact that sine is symmetric about $180°$ . The second quadrant angle will be $180° - 60° = 120°$ . This is the second solution.
Check for Other Solutions: Check for any other angles within the range 0^\circ \leq \theta < 360^\circ that might have the same sine value. Since the sine function repeats every $360^\circ$ , and the problem only asks for angles within one full rotation, there are no more solutions.