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Solve for sin x= √3/2

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Answer:

x = 60° and x = 120°

Explanation:

To solve the equation sin x = √3/2, we need to determine the values of x that satisfy this equation.

We know that sin x = opposite/hypotenuse, where x is an angle in a right triangle. In this case, sin x = √3/2, which means that the opposite side of the angle x is √3 and the hypotenuse is 2.

We can use the Pythagorean theorem to find the length of the adjacent side of the triangle:

a^2 + b^2 = c^2

a^2 + (√3)^2 = 2^2

a^2 + 3 = 4

a^2 = 1

a = ±1

So the adjacent side of the triangle is either 1 or -1. Since sin x is positive and √3/2 is positive, we know that x is in either the first or second quadrant.

In the first quadrant (0° < x < 90°), sin x is positive and the adjacent side is positive, which means that x is 60°.

In the second quadrant (90° < x < 180°), sin x is positive and the adjacent side is negative, which means that x is 120°.

Therefore, the solutions to the equation sin x = √3/2 are x = 60° and x = 120°.

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