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Example Questions
Example Question #71 : Trigonometric Identities
Simplify using identities. Leave no fractions in your answer.
The easiest first step is to simplify our inverse identities:
Cross cancelling, we end up with
Finally, eliminate the fraction:
Thus,
Example Question #1 : Identities Of Inverse Operations
Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.
1.
Using the quotient identities for trig functions, you can rewrite,
and
Then the fraction becomes
Example Question #3 : Identities Of Inverse Operations
Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.
Use the Pythagorean Identities:
and
Thus the expression becomes,
.
Example Question #1 : Identities Of Inverse Operations
Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.
Use the distributive property (FOIL method) to simplify the expression.
Using Pythagorean Identities:
.
Example Question #71 : Trigonometry
Simplify each expression below. Your answer should have (at most) one trigonometric function and no fractions.
First, simplify the first term in the expression to 1 because of the Pythagorean Identity.
Then, simplify the second term to
.
This reduces to
.
The expression is now,
.
Distribute the negative and get,
.
Example Question #71 : Trigonometric Identities
Solve each question over the interval
Divide both sides by to get
.
Take the square root of both sides to get that and
.
The angles for which this is true (this is taking the arctan) are every angle when and
.
These angles are all the multiples of .
Example Question #71 : Trigonometric Identities
can be stated as all of the following except...
Let's look at these individually:
is true by definition, as is
.
is also true because of a co-function identity.
This leaves two - and we can tell which of these does not work using the fact that , which means that
is our answer.
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