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Example Questions
Example Question #2 : Solve Trigonometric Equations And Inequalities In Quadratic Form
Solve when
There are no solutions.
By adding one to both sides of the original equation, we get , and by taking the square root of both sides of this, we get
From there, we get that, on the given interval, the only solutions are
and
.
Example Question #5 : Sum And Difference Identities
Evaluate the exact value of:
In order to solve , two special angles will need to be used to solve for the exact values.
The angles chosen are and
degrees, since:
Write the formula for the cosine additive identity.
Substitute the known variables.
Example Question #11 : Sum And Difference Identities
In the problem below, and
.
Find
.
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Since and
is in quadrant I, we can say that
and
and therefore:
. So
.
Using the cosine sum formula, we then see:
.
Example Question #12 : Sum And Difference Identities
In the problem below, and
.
Find
.
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Using the cosine difference formula, we see:
Example Question #13 : Sum And Difference Identities
Find using the sum identity.
Using the sum formula for sine,
where,
,
yeilds:
.
Example Question #14 : Sum And Difference Identities
Calculate .
Notice that is equivalent to
. With this conversion, the sum formula can be applied using,
where
,
.
Therefore the result is as follows:
.
Example Question #15 : Sum And Difference Identities
Find the exact value for:
In order to solve this question, it is necessary to know the sine difference identity.
The values of and
must be a special angle, and their difference must be 15 degrees.
A possibility of their values that match the criteria are:
Substitute the values into the formula and solve.
Evaluate .
Example Question #16 : Sum And Difference Identities
Find the exact value of:
In order to find the exact value of , the sum identity of sine must be used. Write the formula.
The only possibilites of and
are 45 and 60 degrees interchangably. Substitute these values into the equation and evaluate.
Example Question #14 : Sum And Difference Identities
In the problem below, and
.
Find
.
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Using the sine sum formula, we see:
Example Question #21 : Trigonometric Identities
In the problem below, and
.
Find
.
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Since and
is in quadrant I, we can say that
and
and therefore:
.
So .
Using the sine difference formula, we see:
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