How to Solve Trig Problems

Series Summary

Mathematics is used in virtually every aspect of everyday life. From the basic rules of counting, calculating and measuring to complicated theorems and formulas, math forms the basis for what is absolutely known fact. Incorporating elements of logic and abstraction, mathematics is found in many career fields such as the natural sciences, the medical field, engineering and even music. In this free video series on mathematics, an experienced high school teacher discusses fractions, equations and mathematical problem solving skills. Find out how to solve inequalities, double inequalities and linear equations. Get tips for understanding and writing fractions, and learn the basics of reading a ruler. Solve any mathematical problem with these helpful online math lessons.

Video Transcript

"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."