# How can i solve this (trigonometry)?

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#(sinx-1/2)(sinx-2)<=0# over the interval #[0;2pi]#

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#### Explanation

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*Alternate answer, using the quadratic formula, as requested.*

First, find where the left hand side is *equal* to

#=(5/2+-sqrt(9/4))/2#

#=(5/2+-3/2)/2#

#=5/4+-3/4#

(Note that we could have arrived at this conclusion directly from the factored form by setting each factor equal to

As

Using knowledge of common angles, a unit circle, or a calculator, we find that

As

and the sign of

With that, we can determine the sign of

Thus

Thus

Thus

Adding in the points at which the function is

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#### Explanation

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#### Answer:

#### Explanation:

Note first that as

Thus, the given problem is equivalent to the problem

Adding

Using the unit circle, we can tell that on our restricted interval, we have

Describe your changes (optional) 200