# Please solve q 11?

##### 2 Answers

Find the minimum value of

The linear combination is a phase shifted and scaled sine wave, the scale determined by the magnitude of the coefficients in polar form,

#### Explanation:

Find the minimum value of

The linear combination of sine and cosine of the same angle is a phase shift and a scaling. We recognize the Pythagorean Triple

Let

so has a minimum of

#### Explanation:

Divide the equation

are the coefficients of

Let

Now,

The value of

So, the minimum value of