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Hi, I'm Steve Jones and I'm going to tell you how to solve trigonometric problems. Well
the first thing we have to understand is that it's all based on right angle triangles, we've
got the right angle triangle here, side adjacent to the angle thirty degrees opposite to the
angle thirty degrees and the hypotenuse of the right angle triangle which is opposite
the right angle. Okay, we're using the angle thirty degrees because we know sine is thirty
degrees is an easy one. It is in fact a zero point five. So if we actually want to solve
a problem, if we know the length of the hypotenuse, for example, let this hypotenuse be three
centimeters, we don't know the length of this side, we don't know the length of that side,
but we don't have to because in the right angle triangle they are fixed. We would therefore
say that sin thirty degrees is equal to the length of the side opposite, just write that
just opp. Divide it by the hypotenuse, hyp. All right. And obviously, we know the hypotenuse,
we don't know the opposite side, that's what we'd like to work out. So, the hypotenuse
is three. But we know that sine thirty is zero point five. So we end up with an equation
zero point five is equal to the side opposite divided by three. And if we multiply both
sides by three, then one point - zero point five times three is one point five, will be
equal to the opposite multiplied by three is the length of the opposite side. So the
opposite side is of length one point five centimeters. It's half the length of the hypotenuse.
Now that is a simple right angle triangle and we can work out the other values. But
remember we have three different functions, we have a sine function, a cosine function
and a tangent. Cosine is the adjacent length, the adjacent side divided by the half hypotenuse,
and the tangent is the opposite over the adjacent. So for a right angle triangle, once we have
the length of the hypotenuse and an angle we can work out of the length of any of the
other sides using these formulations. Where do we get the actual numbers for sine, well,
if you look on your calculator, you put in the number thirty and press the sine it'll
give you zero point five, it'll tell you what the value is, if you put in forty five you'll
get a different value. So you can work out the value that way, or you can use sine tables,
these have been used for hundreds of years. They're well documented, it's very easy to
do. Right now with other triangles, that don't have a right angling, we've got angles A,
B and C and sides little A, little B and little C. Now we have a rule for this. And it's called
the sine rule. A over sine A is equal to B over sine B equals to C over sine C. What
this means is that if we are given three of these variables for example A, sine A and
sine B, then we can calculate B. Or if we're given B, C and sine B then we can calculate
sine C. So what it enables us to do is within this particular system with any triangle,
we can work out the length of a side or the angle providing we have the opposite sides
or the angles associated with those sides. So this in brief is how to solve trigonometric
problems.