Are you lost whenever someone says "Trig"? Or "Pythagorean"? Relax, it isn't as hard as it sounds. This site will help you learn to solve all sorts of identities, including Pythagorean. Click a link to get started, after you read the lesson.
Solving equations means finding X. That is what solving equations means. It's the same for Trig equations. Identities are equations that some math genius thought up who knows how long ago that we get to use today to help us solve equations in much less time. On this site, we will use about half of these identities. We will use the reciprocal ( the simple ones), quotient (the useful ones), Pythagorean (the unique ones), Cofunction (the interesting ones), and the Even/Odd (the easy ones) Identities. The real trick, though is to keep trying different things if one fails.
The best way to solve these equations is by rearranging the problem till you have one function with one answer. Once you do this, you find all the solutions in the given frame. For example: If you have a problem like 1/sin(X)=2, what you do is you turn the 1/sin(x) into csc(X) and then it becomes csc(X)=2. This looks familiar, doesn't it? It's part of the unit circle chart. So you find out that X=30 °. but that isn't the only place csc(X)=2. It could also be 150 °, or 350 °, or 510 ° and so on! How do we write that? At what point do we stop? Mathematicians decided that there had to be a way to deal with this. So they decided that we can do 2 things. 1: the problem could have a limit (normally 0 ° to 360 °) or 2: we could add a finishing touch that covers the many possibilities of full circles. We add "+360k ° " to the end of the equation. Many times they put it in radians (they think it makes them cool or something) but for the time being, we will stay in degrees and you can convert them if necessary. And that's it. So for our problem, because the Questioner didn't add a limit, the answer has to be X=30 °+360k °, 150 °+360k°
The best way to solve these equations is by rearranging the problem till you have one function with one answer. Once you do this, you find all the solutions in the given frame. For example: If you have a problem like 1/sin(X)=2, what you do is you turn the 1/sin(x) into csc(X) and then it becomes csc(X)=2. This looks familiar, doesn't it? It's part of the unit circle chart. So you find out that X=30 °. but that isn't the only place csc(X)=2. It could also be 150 °, or 350 °, or 510 ° and so on! How do we write that? At what point do we stop? Mathematicians decided that there had to be a way to deal with this. So they decided that we can do 2 things. 1: the problem could have a limit (normally 0 ° to 360 °) or 2: we could add a finishing touch that covers the many possibilities of full circles. We add "+360k ° " to the end of the equation. Many times they put it in radians (they think it makes them cool or something) but for the time being, we will stay in degrees and you can convert them if necessary. And that's it. So for our problem, because the Questioner didn't add a limit, the answer has to be X=30 °+360k °, 150 °+360k°
