How to Solve Trigonometric & Circular Function Word Problems

Hi, I'm Rachel, and today we're going to be going over how to solve trigonometric function in circular function word problems. So, we use a lot of trig function word problems when we have something like perhaps a flag pole that maybe cast a certain shadow on the ground, right? And we want to find out maybe the length of the shadow for example. So we know that the flag pole is 10 feet tall, and we know that the angle here that it's forming is maybe 30 degrees, and we want to find the length of the shadow. So, we know that we can use our trigonometric functions, right? We have sin, cosin and tangent are the three main ones. So here we have the opposite of 30 degrees, the opposite leg next to the adjacent leg. So that's going to be tangent. So, that is tangent of, that's going to be 10 over x, equals tangent of 30 degrees. So, then we can multiply both sides by x, right? To get the x out of the denominator, because we don't like it there. So then we can have 10 equals tan of 30 degrees times x, and then we divide by tan of 30 degrees so that we isolate the x by itself. And x is going to be 10 over tan of 30, which we could just find out when we plug it into our calculator. And that is how to solve a trigonometric function word problem. Now a circular word problem, that can involve anything in a circle, it could be something like, you know you're trying to find out what's the area of a certain sample of this circle so that you can, you know, put wrapping paper just on this, the surface of it for example. So, in that problem you're going to use the area of a circle, pi r-squared. Let's say that you know that the radius is 10. Well then the area is going to be pi times r-squared, which is 10 squared, which is 100, so 100 pi. And make sure you always use the units, so maybe this is in feet squared, so make sure for area it's always squared. And that's an example of a word problem with a circle, and an example of a word problem with a trigonometric function. I'm Rachel, and thank you for learning with me today.