Ok, after being out of school for almost 10 years I am now in college and VERY rusty with even the most basic Algebra.
I say this so you know that I understand the concepts of the trig we are learning, and how they arrive at the solutions in most cases....but in the following problem, there is one step that I can't figure out how the book is arriving at.....
2 sin² t + sin t - 3 / 1 - cos² t - sin t
Now we substitute 1 - cos² t for sin² t and get....
2 sin² t + sin t - 3 / sin² t - sin t
I get that. Now the next step is what I don't get. The next step says "Factoring in both the numerator and the denominator" and this is the equation.....
(2 sin t + 3) (sin t - 1) / sin t (sin t - 1)
Then they show strike-through lines across both of the (sin t -1) 's. The concept is factoring out like-expressions if you have 1 on the top and 1 on the bottom of a quotient. So I get the 4th step too. It's just that 3rd step, how they arrived at that baffles me.
Can anyone help? Please explain the step like you are teaching 9th grade algebra, because I'm VERY rusty! Thanks in adance!
Best answer goes to the FIRST correct answer! :D
I say this so you know that I understand the concepts of the trig we are learning, and how they arrive at the solutions in most cases....but in the following problem, there is one step that I can't figure out how the book is arriving at.....
2 sin² t + sin t - 3 / 1 - cos² t - sin t
Now we substitute 1 - cos² t for sin² t and get....
2 sin² t + sin t - 3 / sin² t - sin t
I get that. Now the next step is what I don't get. The next step says "Factoring in both the numerator and the denominator" and this is the equation.....
(2 sin t + 3) (sin t - 1) / sin t (sin t - 1)
Then they show strike-through lines across both of the (sin t -1) 's. The concept is factoring out like-expressions if you have 1 on the top and 1 on the bottom of a quotient. So I get the 4th step too. It's just that 3rd step, how they arrived at that baffles me.
Can anyone help? Please explain the step like you are teaching 9th grade algebra, because I'm VERY rusty! Thanks in adance!
Best answer goes to the FIRST correct answer! :D
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Think of the numerator as 2X^2 + X - 3 where X = sin t. Factorise the quadratic and hey presto.
Same for the denominator.
Good luck.
Same for the denominator.
Good luck.