How do you solve this without using a calculator?

Question

i need to find the value of the expression cos pi without using a calculator. i checked my notes but im still confused. help?

Answer 1

cos(pi) = 0

sin(pi) = -1

Well, those are very standard values. You can look up those standard values in the Unit circle.

look at this:

http://en.wikipedia.org/wiki/Image:Unit_...

It is a confusing picture, I know, but take your time to discover how it works. When you understand, this math will be easier for you!

this is the Unit circle. Imagine a line starting at O (the middle), ending at (1,0). This line will rotate anticlockwise, it's end will draw the circle you see.

the angle the line makes with the right part of the x-axis can be measured in Pi or in degrees (as you see in the picture, inside the circle)

The y value of the end of our rotating line is it's sin value.

The x value of the end of our rotating line is it's cos value.

Pff, hard story huh! ask your math teacher if you don't get it.

So, for example:

sin(0,5 pi) = ?

for this question we can use the unit circle.

At an angle of 0,5 pi the line is vertical, so the point at the end is at (0,1) which makes it's y-value 1

so the answer is 1

Answer 2

cos pi = -1.

Remember the cosine curve.  cos 0 = 1, cos π/2 = 0, cos π = -1

Answer 3

While that method works, a more precise way to check cosine values of a function when the value doesn't fall on an exact increment of the unit circle is to compute the taylor polynomial.

This is a fairly easy function to work with - even without a calculator.

For example:  Cos (X) can be represented as (forgive the bad notation):  ÃƒÂ¢Ã‚ˆÂ‘(-1)^k•(x^2k)/(2k)!  with k=number of partial sums computed.

Answer 4

pi is same as 180 degrees

kosine(180 deg)=-kosine(0)=-1

Answer 5

cosπ is the same as cos 180°. That is -1

Answer 6

pi is 180 degrees so cos pi is -1. Look at a graph of the cos function.