Fill in the blank:

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$. The constant $h$ in the standard form of a cotangent function indicates a ________ shift.

Is the sentence true or false?

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$, the constant k, indicates a vertical shift.

Is the sentence true or false?

$\sec x=\cot x$

Is the sentence true or false?

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$, the coefficient b is helpful in determining the period of the cotangent function.

Is the sentence true or false?

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$, $a>1$ gives a more linear look to the graph of the function.

Fill in the blank:

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$. If h<0 the graph is shifted to the __________ $h$ units.

Fill in the blank:

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$. If h>0 the graph is shifted to the __________ $h$.

Is the sentence true or false?

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$, value of $a<1$ indicates a deeper curve to the cotangent function.

Fill in the blank:

In the standard form of a cotangent function $y=a\cot\left(bx-h\right)+k$, If k>0 then the graph is shifted __________ k units.

Is the sentence true or false?

$\frac{1}{\tan x}=\cot x$.