Question

Determine exact value of cos(cos^-1(19 pi)).

is this the cos (a+b)= cos a cos b- sina sin b? or is it something different. When plugging it in the calculator, do we enter it with cos and then the (cos^-1(19 pi)).

Answer 1

[AI-generated answer — Explain Bot]

To determine the exact value of cos(cos^-1(19π)), we can use the concept of inverse trigonometric functions.

First, let's focus on the expression cos(cos^-1(19π)). The inverse cosine function, cos^-1, or arccosine, returns the angle whose cosine is the given value. So, in this case, cos^-1(19π) returns an angle whose cosine is 19π.

Next, we can use the identity cos(cosθ) = θ to simplify the expression. Since we have cos(cos^-1(19π)), we can conclude that cos^-1(19π) is the angle itself.

So, the exact value of cos(cos^-1(19π)) is just 19π.

Regarding the cosine addition formula, cos(a + b) = cos(a)cos(b) - sin(a)sin(b), it is not applicable in this case since we are not dealing with a sum of angles. Therefore, we cannot use that formula here.

When using a calculator to evaluate cos(cos^-1(19π)), you need to use the functions correctly. Most calculators have the inverse cosine function labeled as "cos^-1" or "arccos." To plug in the expression, you would enter "cos(arccos(19π))." This will return the exact value of 19π in radians.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the exact value of cos(cos^-1(19 pi)), we can use the identity:

cos(cos^(-1)(x)) = x

In this case, x = 19 pi.

Plugging in the value, we get:

cos(cos^(-1)(19 pi)) = 19 pi

So, the exact value of cos(cos^-1(19 pi)) is 19 pi.

Regarding your second question, when entering it into a calculator, you should first calculate the inverse cosine of 19 pi (cos^(-1)(19 pi)) and then find the cosine of that result. The specific sequence of buttons may vary depending on the calculator you are using.

Answer 3

an even number of pi is all the way around,360 degrees

and odd number of pi leaves you at 180, the negative x axis
the cos there at (-1,0) on theta = 180 degrees is -1