Module 6: Lesson 4 Using Trigonometric Identities Part 2-­‐Double Angle Identities Video Transcript Hey everyone, this is a video for module 6 lesson 4, using trig identities. We are in the part 2 notes, I am going to do an example using the double angle identity. So this example says, given that sine of 23 degrees is .391, and the cosine of 23 degrees is .921 and the tangent of 23 degrees is .424, find the value of sine of 46 degrees, cosine of 46 degrees, and tangent of 46 degrees. So, we are going to find the sine of 46 degrees first. The double angle identity says the sine of 2 theta which is your angle is going to equal 2 sine of theta times the cosine of theta. So if I am trying to find the sine of 46 that could be rewritten as the sine of 2 times 23 and since 23 is my angle now I can do 2 times the sine of 23, excuse me, I could do 2 times the sine of theta, I am going to go ahead and plug that in there, 2 times the sine of theta which theta is 23, the sine of 23 is .391 times the cosine of theta which cosine of 23 which is .921. I am going to pull my calculator up. I am going to make sure that I am in degrees, oh that doesn’t matter because I already have the numbers there, forgot that. So just plug it in 2 times .391 times .921 and hit enter. So that answer is going to be .720 approximately, approximately .720. So the sine of 46 is approximately .720. Ok, now if we go ahead and do the cosine of 46 its going to be the same process here, if I have the cosine of 46 that can be written as the cosine of 2 times 23. Now if you look back in your notes there’s three different ways to find this. So I am going to use the middle one that says this would equal 2 times the cosine of squared, cosine squared of theta and theta in this problem is 23 minus 1. So I need to know what the cosine of 23 is and the cosine of 23 is .921. So that’s 2 times .921 minus one. Go ahead and put that in the calculator, so 2 times, oh I forgot my square over here, I do have to square the cosine of 23. So 2 times .921 squared minus 1. Go ahead and hit enter there, and I get approximately. 696.
Ok, and now for the last one, tangent of 46. I do the tangent of 46, that’s like writing tangent of 2 times 23, the double angle identity which it says I could do 2 times the tangent of theta and theta is 23, so the tangent of 23 would go on top over 1 minus tangent squared 23. Let me see what the tangent of 23 was, .424, so that is going to go in as .242, no, .424 excuse me, .424 over 1 minus, tangent of 23 is .424, so .424 squared. All right make sure you put all your parenthesis in here correctly, the numerator needs to go in a set of parenthesis, 2 times .424 close the parenthesis around the numerator divide by, open another parenthesis 1 minus .424 squared close that parenthesis, enter. My answer is approximately 1.034. And that’s the tangent of 46. And that’s how you can use the double angle identities.