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Example Questions
Example Question #31 : Trigonometric Identities
Evaluate
.
is equivalent to
or more simplified
.
We can use the sum identity to evaluate this sine:
From the unit circle, we can determine these measures:
Example Question #32 : Trigonometric Identities
Evaluate
.
The angle or
.
Using the first one:
We can find these values in the unit circle:
Example Question #31 : 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 tangent sum formula, we see:
Example Question #32 : 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 tangent sum formula, we see:
Example Question #32 : Trigonometric Identities
Given that and
, find
.
Jump straight to the tangent sum formula:
From here plug in the given values and simplify.
Example Question #21 : Sum And Difference Identities
Which of the following expressions best represents ?
Write the identity for .
Set the value of the angle equal to .
Substitute the value of into the identity.
Example Question #33 : Trigonometric Identities
Find the value of .
To solve , we will need to use both the sum and difference identities for cosine.
Write the formula for these identities.
To solve for and
, find two special angles whose difference and sum equals to the angle 15 and 75, respectively. The two special angles are 45 and 30.
Substitute the special angles in the formula.
Evaluate both conditions.
Solve for .
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