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Apr 1
To solve sin x = 1/2, you can use the unit circle or a calculator to find the values of x that satisfy this equation.
1. Using the unit circle:
- Recall that the sine function is positive in the first and second quadrants.
- In the first quadrant, sin(30°) = 1/2. So, x = 30° or π/6.
- In the second quadrant, sin(150°) = 1/2. So, x = 150° or 5π/6.
Therefore, the solutions to sin x = 1/2 are x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.
2. Using a calculator:
- You can use the inverse sine function (sin^-1) on a calculator to find the values of x that satisfy sin x = 1/2.
- sin^-1(1/2) = 30° or π/6.
- Therefore, the solutions to sin x = 1/2 are x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.
These are the two methods you can use to solve sin x = 1/2.
1. Using the unit circle:
- Recall that the sine function is positive in the first and second quadrants.
- In the first quadrant, sin(30°) = 1/2. So, x = 30° or π/6.
- In the second quadrant, sin(150°) = 1/2. So, x = 150° or 5π/6.
Therefore, the solutions to sin x = 1/2 are x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.
2. Using a calculator:
- You can use the inverse sine function (sin^-1) on a calculator to find the values of x that satisfy sin x = 1/2.
- sin^-1(1/2) = 30° or π/6.
- Therefore, the solutions to sin x = 1/2 are x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.
These are the two methods you can use to solve sin x = 1/2.
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