Question 51942
These are problems about radian measure, which is just another way of
measuring angles.
You have to picture certain things, or you just wont get it. Get these
mental pictures first. Forget numbers, mostly. Forget trig. Just poicture
things in your head.
A radius is a string fastened at one end and pulled tight. Then you
mark a starting point on the ground where the other end is.
You walk this string around in a circle until you come back to
the mark you made on the ground. You just went around 360 degrees,
and you're back where you started.
Do you recall the formula for circumference of a circle?
It's {{{C = 2*pi*r}}} where {{{pi}}} = 3.141 and r is the radius.
Suppose {{{r = 1}}} Then {{{C = 2*pi}}}, right?
That's what is meant by the unit circle. The radius is one.
You just went around in a circle 360 degrees and came back to
where you started, right? What if I call the 360 degrees by a different 
name? What if I call it {{{2*pi}}} RADIANS? Don't be afaid of the name.
It's no more scary than degrees. 
{{{2*pi}}} radians for a full circle works out good because, as I
showed you, with a radius = 1, the circumference measures {{{2*pi}}}.
You just use this instead of 360 degees.
So what's half way around the circle?
That's {{{2*pi / 2}}} radians = {{{pi}}} radians
What's 1/4 of the way around the circle?
That's half of half-way = {{{pi / 2}}} radians
That's the key to all these problems. Each problem has 3.14/2 in it
That's the same as {{{pi/2}}}, a quarter of the way around the circle.
(a) sin(-3(3.14)/2)
The minus sign means go in the clockwise direction.
Read it as "Go clockwise three 1/4 turns of the circle from zero point
Where do you end up?
(b)sin(133(3.14)/2) 
"Make 133 1/4 turns around the circle going COUNTER-clockwise from zero."
The big number 133 is not the least bit scary. What happens if you make
four 1/4 turns around the unit circle? You're back to zero. So
divide 133 by 4. That's how many times you got back to the zero point.
The remainder is where you end up. {{{133/4 = 33 + 1/4}}}. So,
you're {{{pi/2}}} radians from zero in the COUNTER-clockwise direction.
(c) tan(-49(3.14)/2 
Read like this "Make 49 one-quarter turns in the CLOCK-WISE direction from zero."
Again, divide 49 by 4 to get the number of times you go back to zero.
The remainder is where you end up, {{{49/4 = 12 + 1/4}}}.
Remember, you're {{{pi/2}}} radians in the clockwise direction from zero now
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That's the hardest part. Now Use the rules of trig to solve each one.
For example, 
(a) sin(-3(3.14)/2) What's the sin{{{pi/2}}} where you ended up? It's +1
(b) sin(133(3.14)/2) What's the sin{{{pi/2}}} where you ended up? It's also +1
Picturing the trips around the circle and getting the direction right is
the challenge. The rest is know trig facts and applying them.