Double-Angle Formula Made EASY | Find sin(2x) Fast!

Added: 2026-06-02

[00:00:00]One formula, four lines of work, full marks. Today, I will show you exactly uh how the double angle formula turns a tricky trigonometric question into one of the easiest one on your exam. So, let's first start by reading our question. So, we are given that sin of x is equal to 3/5 and we have x is the first uh is an angle in the first quadrant. Now, the question is find sin of 2x.

[00:00:24]So, sin of 2x is a double angle. It has the double angle formula, which is the topic of this video. So, first of all, let's remember together what is the double angle formula. It is sin of 2x is equal to 2 sin x * cos x. And here is the double angle formula that you should always remember.

[00:00:45]Next is what? Next is to notice that we don't have cos x, we have sin x. So, now the question is to find cos x. To be able to find the value of cos x, we're going to use the previous value that we have, which is sin x, and we going to plug it in inside the identity that we all know, which is that sin of x squared + cos of x squared is equal to 1.

[00:01:10]So, cos of x squared is equal to 1 sin of x squared, which is 1 3/5 squared, which is what? Which is uh 25 over 25 - 9/25, which is 16/25.

[00:01:29]And here we got cos squared x, but in the formula in the double angle formula, we needed cos x and not double not cos squared x. So, cos x is what? Is square root of this, so it is 4/5. And here we got our second value. So, now we can plug everything inside the double angle formula. So, sin of 2x, it is what? It is 2 * 3/5 * what? * 4/5.

[00:01:57]And this will lead to 24 over 25.

[00:02:01]And the double sign the double sign double angle formula led to 24 over 25.

[00:02:08]Now, a quick example. Whenever you are given sign or cosine alone, always use the identity, this one that I will show you here. So, always use this identity when you want to solve these questions because it will it will help you a lot to find the second one, to find the missing value. Always pay attention to the quadrant because it determines the sign. If you enjoy these types of videos, please consider liking my video, follow me on TikTok, follow me on YouTube, and reposting this video on YouTube on TikTok. And Professor Kartush will see you in the next one. Bye-bye.