HELP EDG 2020 Which half of the unit circle satisfies the trigonometric inequality cos Ø >0? Assume that ø is the angle made by the
positive x-axis and a ray from the origin.
O the top half
O the bottom half
O the right half
O the left half

the right half

Step-by-step explanation:

We know that cosine is a pair function.

This means that:

Cos(a) = Cos( -a)

We also know that:

Cos(pi) = 0

then:

Cos(-pi) = 0

pi and -pi are located in the y-axis, so from this we can know that the cosine function will be always positive on the right side, or in the left side, we can discard the other two options.

Now, we also know that cos(0) = 1.

And:

-pi < 0 < pi

So the two zeros are at the y-axis, and we know that cos(0) is positive (the angle 0 would be on the positive side of the x-axis, at the right), then all the right side must be positive.

Then the correct option is:

the right half

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are