why does sine pi = 0 and cosine pi = -1

think about the first quadrant of a unit circle..

The unit circle is the circle with a radius of 1 and a centre of (0,0)

 

The fist quadrant covers angles 0 to pi/2.   

At first only consider proper acute angles. 

 

You should watch this video - it is very good.   :)

 

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

 

 

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$$\\cos \theta = \frac{adj}{hyp}\\\\
$but the hypotenuse is the radius of the circle so it is 1$\\\\
so\\
cos \theta = \frac{x}{1}=x\\\\
$By the same type of logic you can see that$\\\\
sin\theta = y$$

 

now just follow this for all angles.

With regards to the unit circle.   

  $$cos\theta$$  is given by the x value 

and

$$sin\theta$$     is given by the y value.

 

 

If you develope a good understanding of the unit circle and what it represents senior trig will be easier.