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#mathematics
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#trigonometry
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#acute-angles
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How to solve sin x =1/2 where the angles are acute?
Anonymous
more than 4 weeks ago
How to solve sin x =1/2 where the angles are acute?
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ChatGPT
more than 4 weeks ago
To solve sin x = 1/2 where the angles are acute, you can use the unit circle or reference angles to find the solutions.
1. First, identify the reference angle for sin x = 1/2. The reference angle for sin x = 1/2 is 30 degrees or π/6 radians. This is because sin 30 degrees = 1/2.
2. Since sin is positive in the first and second quadrants, the solutions for sin x = 1/2 in the acute angles will be in the first and second quadrants.
3. In the first quadrant, the angle that satisfies sin x = 1/2 is 30 degrees or π/6 radians.
4. In the second quadrant, the angle that satisfies sin x = 1/2 is 150 degrees or 5π/6 radians.
Therefore, the solutions for sin x = 1/2 in the acute angles are x = 30 degrees or π/6 radians and x = 150 degrees or 5π/6 radians.
1. First, identify the reference angle for sin x = 1/2. The reference angle for sin x = 1/2 is 30 degrees or π/6 radians. This is because sin 30 degrees = 1/2.
2. Since sin is positive in the first and second quadrants, the solutions for sin x = 1/2 in the acute angles will be in the first and second quadrants.
3. In the first quadrant, the angle that satisfies sin x = 1/2 is 30 degrees or π/6 radians.
4. In the second quadrant, the angle that satisfies sin x = 1/2 is 150 degrees or 5π/6 radians.
Therefore, the solutions for sin x = 1/2 in the acute angles are x = 30 degrees or π/6 radians and x = 150 degrees or 5π/6 radians.
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