Factoring Trigonometric Equations - Trigonometry
Card 0 of 12
Factor 
.
Factor
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 
.
Don't get scared off by the fact we're doing trig functions! Factor as you normally would. Because our middle term is negative (
This means that
Compare your answer with the correct one above
Find the zeros of the above equation in the interval
.
Find the zeros of the above equation in the interval
Therefore,
and that only happens once in the given interval, at 
, or 45 degrees.
Therefore,
and that only happens once in the given interval, at
Compare your answer with the correct one above
Which of the following values of 
in radians satisfy the equation
Which of the following values of
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.
The fastest way to solve this equation is to simply try the three answers. Plugging in
Our first choice is valid.
Plugging in
However, since
Finally, plugging in
Therefore, our third answer choice is not correct, meaning only 1 is correct.
Compare your answer with the correct one above
Factor the following expression:
Factor the following expression:
Note first that:
and :
.
Now taking 
. We have
.
Since 
and 
.
We therefore have :
Note first that:
Now taking
Since
We therefore have :
Compare your answer with the correct one above
Factor the expression
Factor the expression
We have 
.
Now since 
This last expression can be written as :
.
This shows the required result.
We have
Now since
This last expression can be written as :
This shows the required result.
Compare your answer with the correct one above
Factor the following expression
where 
is assumed to be a positive integer.
Factor the following expression
Letting 
, we have the equivalent expression:
.
We cant factor 
since 
.
This shows that we cannot factor the above expression.
Letting
We cant factor
This shows that we cannot factor the above expression.
Compare your answer with the correct one above
Factor
Factor
We first note that we have:
Then taking 
, we have the result.
We first note that we have:
Then taking
Compare your answer with the correct one above
Find a simple expression for the following :
Find a simple expression for the following :
First of all we know that :
and this gives:
.
Now we need to see that: 
can be written as
and since 
we have then:
.
First of all we know that :
Now we need to see that:
we have then:
Compare your answer with the correct one above
Factor the following expression:
Factor the following expression:
We know that we can write
in the following form
.
Now taking 
,
we have:
.
This is the result that we need.
We know that we can write
Now taking
we have:
This is the result that we need.
Compare your answer with the correct one above
What is a simple expression for the formula:
What is a simple expression for the formula:
From the expression :
we have:
Now since we know that :
. This expression becomes:
.
This is what we need to show.
From the expression :
we have:
Now since we know that :
This is what we need to show.
Compare your answer with the correct one above
We accept that :
What is a simple expression of
We accept that :
What is a simple expression of
First we see that :
.
Now letting 
we have
We know that :
and we are given that
, this gives
First we see that :
Now letting
we have
We know that :
Compare your answer with the correct one above
Factor: 
Factor:
Step 1: Recall the difference of squares (or powers of four) formula:
Step 2: Factor the question:
Factor more:
Step 3: Recall a trigonometric identity:
.. Replace this
Final Answer: 
Step 1: Recall the difference of squares (or powers of four) formula:
Step 2: Factor the question:
Factor more:
Step 3: Recall a trigonometric identity:
Final Answer:
Compare your answer with the correct one above