Factoring Trigonometric Equations
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Trigonometry › Factoring Trigonometric Equations
Factor .
Explanation
Don't get scared off by the fact we're doing trig functions! Factor as you normally would. Because our middle term is negative (), we know that the signs inside of our parentheses will be negative.
This means that can be factored to
or
.
Which of the following values of in radians satisfy the equation
1 only
2 only
3 only
1 and 2
1, 2, and 3
Explanation
The fastest way to solve this equation is to simply try the three answers. Plugging in gives
Our first choice is valid.
Plugging in gives
However, since is undefined, this cannot be a valid answer.
Finally, plugging in gives
Therefore, our third answer choice is not correct, meaning only 1 is correct.
Find the zeros of the above equation in the interval
.
Explanation
Therefore,
and that only happens once in the given interval, at , or 45 degrees.
Factor the expression
Explanation
We have .
Now since
This last expression can be written as :
.
This shows the required result.
Factor the following expression:
Explanation
We know that we can write
in the following form
.
Now taking ,
we have:
.
This is the result that we need.
We accept that :
What is a simple expression of
Explanation
First we see that :
.
Now letting
we have
We know that :
and we are given that
, this gives
Factor the following expression:
We can't factor this expression.
Explanation
Note first that:
and :
.
Now taking . We have
.
Since and
.
We therefore have :
Factor the following expression
where
is assumed to be a positive integer.
We cannot factor the above expression.
Explanation
Letting , we have the equivalent expression:
.
We cant factor since
.
This shows that we cannot factor the above expression.
Factor
Explanation
We first note that we have:
Then taking , we have the result.
Find a simple expression for the following :
Explanation
First of all we know that :
and this gives:
.
Now we need to see that: can be written as
and since
we have then:
.