Determine the domain of a trigonometric function - Pre-Calculus

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.

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.

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

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 .

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.

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.

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.

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

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 .

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.

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.

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.

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

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 .

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.

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.

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.

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

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 .