In section 7-6, we learned how to find the inverse of angles. It was one of the easiest things we did in chapter 7 because you could use your calculator for most of it. However, there are a few times where it cannot be done on a calulater, so you still need to know what you are doing.
When you are given a function with ^-1 at the end of it, that means you are going to find the inverse.
ex: tan^-1(#)
or arc tan (#)
The purpose of an inverse is to find where the angle function has a certain value. It is pretty much finding the opposite.
Putting it in your calculator is pretty simple.
ex: sec^-1 (a/b)= sin ^-1(b/a)
csc^-1 (a/b)= sin^-1 (b/a)
cot^-1 (a/b)= tan^-1 (b/a)
When you plug it in, the mode must be in degrees to get the correct answer. Once you get your answer in decimals, you round to the hundreds.
ex: tan^-1 (5) = 78.69
If you are given something that looks like this:
trig^-1 (trigx)= x
You need to draw it in the coordinate plane and use a formula to find trig 1.
ex: cos (tan^-1 (4/5))
- you need to graph the fraction on a coordinate plane and draw a triangle connecting it to the origin.
- once it is graphed you need to figure out the other side of the triangle, using the pythagorean triples, you can determine that the other side will be 3.
- the formula for tan is cos is y/r, so your answer will be 4/3
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