CPhill

So we have

Circumference = 2 * pi * radius

190 = 2 * pi * r   And solving for "r," we have

r = 190 / (2 * pi) =  95 / pi   ≈   30.2 units

It just represents the distance that a particular number is from 0 on the number line.

For instance, l -3 l = 3, because -3 is 3 units from 0 on the number line.

And since distance is never negative, the absolute value of something is non-negative.

One use is to determine the distance between a positive and negative number on the number line.

For example, the distance between 10 and -7 on the number line can be represented by

l 10 l + l -7 l =

10 + 7  =

17

"Cancelling" the zeroes, we get

166/186  Which, factoring the top and the bottom, we have

(2*83) / (2*93)   And cancelling the "2s," we have

83/93

None....that I could find.....

OK....I'll be serious......

1,000,000 / 8 = 125,000

Given the turbulent history of the Swiss....it's hard to determine......however, we DO know that they were descended from the House of Burger, first ruled by the man shown below. He's best known for his "Swiss Cheese Proclamation" - a decree that allowed the citizenry to "have it their way."

C'mon folks....let's be reasonable here.....don't you think, maybe, that the questioner accidentally hit the "u" key rather than the "i" key....since they are next to each other on the keyboard??

I believe my answer is just fine.........if we allow for a few hunan foibles along the way.....

Ok...so we have this........

y = ax² + 4      ....... and we need to find "a"

So we have

-1 = a(-10)² + 4

-5 = a (100)

(-1/20) = a      .......  So we have ..........

y = (-1/20)(x- 0)² + 4   or just  (-1/20)x² + 4

Note that this parabola opens downward...That makes sense since the vertex is above the x axis and the parabola passes through a point below the x axis.

One half-angle identity for the tangent is given by

tan (a/2) = (1 - cos a) / sin a

So....a, in this case, is 150 degrees.   And we have

tan (75) = tan (150/2) = ( 1 - cos 150) / sin (150) = [1 - (-√3/2)] / (1/2) = [1 + √3/2] / (1/2) =

2 [ 2 + √3] / 2 = [ 2 + √3] ≈ 3.732

Note...the same result could have been obtained by using the tangent angle sum identity with the angles 30 degrees and 45 degrees.

Welcome to the club !!

Good job on that answer !!

OK...let's look at the first one....notice that it's a 45 degree reference angle in the 2nd quadrant. Now, let's ask ourselves....where else is the cosine negative??...yup...in the 3rd quadrant

So this angle is a 45 degree reference angle in the 3rd quadrant, i.e., 225 degrees.

As for the second one, it's a little trickier......the tangent is positive in the 1st quadrant and in the 3rd quadrant, because, in the 3rd quadrant, both x and y are negative. So this angle is a 30 degree reference angle in quadrant 3....... i.e., 210 degrees.

Cosecant is the reciprocal of the sine....not the inverse!!  If the sine is defined as y/r, then the csc is just r/y.

Remember that the basic functions return angle values. The inverse functions return the angles themselves.

As for dealing with negative angles.......let me know what you're specifically having trouble with and I'll see what I can do.

I hope I've answered what you've asked....