How do you find sinx=1/2?

3 Answers
Apr 14, 2015

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)

Apr 19, 2015

*Diagram not drawn to scale.

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Mar 15, 2017

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

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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

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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! :)