5

Solve the following....

Question

Solve the following.

Solve the following.



Answers

Solve the following.

We want to compute. Sign of tension in verse of X right here. But remember, panda inverse of X is just some angle so we can use the triangle to determine those The angle didn't see using the trig identities. We know that tension, the angle attention that gave us X. You can write this assed engine of some angle giving us X. This thing on the right hand side is the opposite over the adjacent, So an X over a one. And if we want to compute the high pot mission, we have the tiger and the arm of a right triangle. It's gonna be the square of over the other side squared added together. So then what if we wanted to compute the science of this angle here, which happens to be tangent inverse of X? By this equation, well, it's going to be the opposite, which is X over the adjacent, which is the square root of one plus x ray

Let's find the sign of angers tension X So inverse tangent X means the angle Whose tangent is X and I'm gonna call that angle Fate up now let's draw picture. Suppose we have angle fatal here and we know it's tangent is X that means the opposite over adjacent is X. So if the opposite was X and the adjacent was one, that ratio would be X. Now, if that's the case, what's the length of the high pot news? If we're going to find the sine of the angle, we're going to need the high pot news as well as the opposite. So for now, I'm going to call the high pot news H. And now I'm going to use the Pythagorean theorem to find it. H squared equals one squared plus X squared. So H is the square root of one plus x squared. Okay, so now I confined the sign of angle fada. It would be opposite which is X over high pot news, which is square root of one plus X squared

Engine of sign in reserve X and long. Remember, sine inverse is an angle. In fact, it's an angle that gave us X When we take sign of them. Well, we got X. So let's use our triangles. Helps the time and attention should be sign is actually opposite over hypotheses. So we have X over one Lincoln used with a grant their to determine what they should be. Just like before. We have one squared minus expert. And now, if you want, if I intention of this and go right here, which happens to be a sign and rece thanks, it's kinds of the the opposite. Over the adjacent so X over the square, one minus six words Awesome.

Okay. We want to simplify this expression. Tangent of inverse sign of X in verse. Sign of X means the angle. Who signed his ex? I'm going to call that angle theta, so let's draw a reference triangle for data. So let's suppose this is angle Fada and we know it's sign is X. That means the opposite over high pot news is X so we could make the opposite X and the high pot noose. One X divided by one is X. Now we need the tangent of angle. Fada tangent is opposite over adjacent, so we need to find the length of the adjacent for right now I'm going to call it a and I'm going to use the Pythagorean theorem to find it. A squared plus X squared equals one squared, so a squared equals one minus X squared. So a is the square root of one minus X squared. All right, so now the tangent of that angle is the opposite X over the adjacent square root of one minus X squared


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