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Example Questions
Example Question #1 : Trigonometric Functions
Which of the following is the correct domain of , where
represents an integer?
The cotangent graph only has a period of intervals and is most similar to the tangent graph. The domain of cotangent exists everywhere except every
value since an asymptote exists at those values in the domain.
The y-intercept of 3 shifts the cotangent graph up by three units, so this does not affect the domain.
Therefore, the graph exists everywhere except , where
is an integer.
Example Question #2 : Determine The Domain Of A Trigonometric Function
Please choose the best answer from the following choices.
What is the domain of the following function?
All x values make the function work. Thus, making the domain . They're parentheses instead of brackets because parentheses are used when you can't actually use the specific value next to it. It is impossible to use infinity which makes parentheses appropriate. Brackets are used when you CAN use the specific value next to it.
Example Question #1 : Trigonometric Functions
Please choose the best answer from the following choices.
What is the domain of the following function:
All x values work for the function. Thus, making the domain all real numbers. Parentheses are required because you can never actually use the number infinity.
Example Question #4 : Determine The Domain Of A Trigonometric Function
Please choose the best answer from the following choices.
What is the domain of .
If you look at a graph of the function, you can see that every curve has a vertical asymptote that repeats every radians in the positive and negative x-direction, starting at
radians. Also, the curve has a length that stretches
radians which makes the domain
.
Example Question #1 : Trigonometric Functions
What is the restriction of the domain of the function given by:
For all the answer choices below, is any integer.
has restrictions on its domain such that
, where
is any integer.
To determine the domain for ,
we equate the terms within the secant function and set them equal to the original domain restriction.
Solving for ,
The new domain restriction is:
where
is an integer
Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions
Solve the following:
Rewrite in terms of sine and cosine functions.
Since these angles are special angles from the unit circle, the values of each term can be determined from the x and y coordinate points at the specified angle.
Solve each term and simplify the expression.
Example Question #2 : Find The Value Of Any Of The Six Trigonometric Functions
Find the value of .
Using trigonometric relationships, one can set up the equation
.
Solving for ,
Thus, the answer is found to be 29.
Example Question #3 : Find The Value Of Any Of The Six Trigonometric Functions
Find the value of .
Using trigonometric relationships, one can set up the equation
.
Plugging in the values given in the picture we get the equation,
.
Solving for ,
.
Thus, the answer is found to be 106.
Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions
Find all of the angles that satistfy the following equation:
OR
OR
The values of that fit this equation would be:
and
because these angles are in QI and QII where sin is positive and where
.
This is why the answer
is incorrect, because it includes inputs that provide negative values such as:
Thus the answer would be each multiple of
and
, which would provide the following equations:
OR
Example Question #5 : Find The Value Of Any Of The Six Trigonometric Functions
Evaluate:
To evaluate , break up each term into 3 parts and evaluate each term individually.
Simplify by combining the three terms.
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