Question

How do you find `sinx=1/2`?

Answer 1

Use the trig conversion table and the trig unit circle to solve `sin x = 1/2.`
Trig table gives `sin x = 1/2 = sin (pi/6) --> x_1 = pi/6`.
Trig circle gives another arc `x_2 = 5pi/6` that has the same sin value `(1/2)`.
Since `f(x) = sin x` is a periodic function, with period `2pi`, then there are an infinity of arcs that have the same sin value `(1/2)`, when the variable arc x rotates around the trig unit circle many times. They are called "extended answers".

They are: `x = pi/6 + K*2pi`; and `x = 5pi/6 + K*2pi.` (`K` is a whole number)

Answer 2

*Diagram not drawn to scale.

Answer 3

`30^circ` `and 150^circ`

Explanation:

We can find the answer using a triangle or the unit circle

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Using a right triangle

`color(blue)(sin(theta)=1/2`

As we see in the diagram, `sin(30^circ)` has a opposit and hypotenuse `1 and 2`

So,

`color(green)(rArrsin(30^circ)=1/2`

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Using unit circle

As `30^circ` and `150^circ` has a `sin` of `1/2`,

`color(green)(rArrsin(30^circ)=1/2`

`color(green)(rArrsin(150^circ)=1/2`

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Hope this helps! :)