Đề Xuất 4/2023 # Arctan Excel Functions: Use Atan And Atan2 To Calculate Inverse Tangent # Top 12 Like | Beiqthatgioi.com

# Đề Xuất 4/2023 # Arctan Excel Functions: Use Atan And Atan2 To Calculate Inverse Tangent # Top 12 Like

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There are two functions for calculating the inverse tangent or arctan in Excel. These two functions are ATAN and ATAN2 (“atan” is short for arctangent), and they each have specific uses depending on the desired results that you’d like to obtain and the inputs available. In general, I’d recommend using ATAN if:

You are only concerned with the first quadrant of the unit circle

You don’t know the x- and y-values

However, use the ATAN2 function if:

You want to return angles in all four quadrants of the unit circle

You know the x- and y-values

Using ATAN to Calculate Arctan in Excel

The ATAN function returns a result between -π/2 and π/2 radians (or -90 and 90 degrees), or in other words, in the first and fourth quadrants.

The syntax is:

ATAN(number)

There is only one argument to ATAN: the number from which you want to calculate the inverse tangent. And since there is only one argument, Excel cannot determine which quadrant the solution should be in.

The absolute values of the angles never exceed 90 degrees, and

Values in the second (II) quadrant in column C are now in the fourth quadrant in column F.

Values in the third (III) quadrant in column C are now in the first quadrant in column F.

Plotting the results on the unit circle looks like this:

Since there is only one argument to the ATAN function, Excel calculates the value of y/x before if evaluates the ATAN function.

It cannot determine, then, whether the input to ATAN is negative because the x-value or the y-value is negative. Therefore, it can’t tell if the result should be in the second quadrant or the fourth quadrant, so it just defaults to the fourth quadrant.

Likewise, when the input value is positive, the original quadrant could be either the first (both x and y positive) or third (both x and y negative).

We could use a complex nested IF function to get the results back into all four quadrants, but fortunately Excel has another function called ATAN2 to help us out.

Using ATAN2 to Calculate Arctan in Excel

The ATAN2 function can also be used to calculate the inverse tangent in Excel. This function returns a result between -π and π radians (or -180 and 180 degrees), using all four quadrants. The syntax is:

ATAN2(x_num,y_num)

There are two arguments:

By inputting two values to the function, Excel can determine which quadrant the value belongs in.

Quadrant 1 if both x and y are positive

Quadrant 2 if x is negative and y is positive

Quadrant 3 if both x and y are negative

Quadrant 4 if x is positive and y is negative

So if we use the formula

=DEGREES(ATAN2(x_num,y_num))

We get the following results:

Hopefully, now you understand the limitations of ATAN and when it’s better to use ATAN2 to calculate the inverse tangent or arctan in Excel.

In general, use ATAN if:

You are working only in the first quadrant

You don’t know the x- or y-values

Use the ATAN2 function if:

You need the angles in all four quadrants

The x- and y-values are known

## How To Use The Excel Counta Function

Random list of names

At the core, this formula uses the INDEX function to retrieve 10 random names from a named range called “names” which contains 100 names. For example, to retrieve the fifth name from the list, we use INDEX like this…

Add row numbers and skip blanks

In the example shown, the goal is to add row numbers in column B only when there is a value in column C. The formula in B5 is:

=IF(ISBLANK(C5),””,COUNTA(\$C\$5:C5))

The IF function first checks if cell C5 has…

Cell contains all of many things

The key is this snippet:

ISNUMBER(SEARCH(things,B5)

This is based on another formula (explained in detail here) that simply checks a cell for a single substring. If the cell contains the substring, the formula…

Count cells that are blank

The COUNTBLANK function counts the number of cells in the range that don’t contain any value and returns this number as the result. Cells that contain text, numbers, dates, errors, etc. are not counted. COUNTBLANK is…

Last row in mixed data with no blanks

This formula uses the COUNTA function to count values in a range. COUNTA counts both numbers and text to so works well with mixed data.

The range B4:B8 contains 5 values, so COUNTA returns 5. The number 5 corresponds…

Count unique values

This example uses the UNIQUE function to extract unique values. When UNIQUE is provided with the range B5:B16, which contains 12 values, it returns the 7 unique values seen in D5:D11. These are returned directly to the…

Dynamic named range with OFFSET

This formula uses the OFFSET function to generate a range that expands and contracts by adjusting height and width based on a count of non-empty cells.

The first argument in OFFSET represents the first cell in the…

Running count group by n size

The core of this formula is the COUNTA function, configured with an expanding range like this:

COUNTA(\$B\$5:B5)

As the formula is copied down the column, the range starting with B5 expands to include each new row, and…

Count cells not equal to many things

First, a little context. Normally, if you have just a couple things you don’t want to count, you can use COUNTIFS like this:

But this doesn…

Project complete percentage

In this example if a task is marked “Done”, then it is considered complete. The goal is to calculate the percent complete for the project by showing the ratio of complete tasks to total tasks, expressed as a percentage…

Count sold and remaining

The COUNTA function counts non-blank cells that contain numbers or text. The first COUNTA counts non-blank cells in the range B5:B11 and returns the number 7:

COUNTA(B5:B11)

The second COUNTA function…

Generate random text strings

The new dynamic array formulas in Excel 365 make it much easier to solve certain tricky problems with formulas.

In this example, the goal is to generate a list of random 6-character codes. The randomness is handled by…

Sort by random

The SORTBY function allows sorting based on one or more “sort by” arrays, as long long as they have dimensions that are compatible with the data being sorted. In this example, there are 10 values being sorted, the…

Score quiz answers with key

This formula uses the named range “key” (C4:G4) for convenience only. Without the named range, you’ll want to use an absolute reference so the formula can be copied.

In cell I7, we have this formula:

=SUM(–(C7:G7=…

Reverse a list or range

The heart of this formula is the INDEX function, which is given the list as the array argument:

=INDEX(list

The second part of the formula is an expression that works out the correct row number as the formula is…

## How To Use The Excel Vlookup Function

VLOOKUP is an Excel function to get data from a table organized vertically. Lookup values must appear in the first column of the table passed into VLOOKUP.  VLOOKUP supports approximate and exact matching, and wildcards (* ?) for partial matches.

V is for vertical

The purpose of VLOOKUP is to get information from a table organized like this:

Using the Order number in column B as a lookup value, VLOOKUP can get the Customer ID, Amount, Name, and State for any order. For example, to get the customer name for order 1004, the formula is:

=

VLOOKUP

(

1004

,

B5:F9

,

4

,

FALSE

)

// returns "Sue Martin"

For horizontal data, you can use the HLOOKUP, INDEX and MATCH, or XLOOKUP.

VLOOKUP is based on column numbers

When you use VLOOKUP, imagine that every column in the table is numbered, starting from the left. To get a value from a particular column, provide the appropriate number as the “column index”. For example, the column index to retrieve the first name below is 2:

The last name and email can be retrieved with columns 3 and 4:

=

VLOOKUP

(

H3

,

B4:E13

,

2

,

FALSE

)

// first name

=

VLOOKUP

(

H3

,

B4:E13

,

3

,

FALSE

)

// last name

=

VLOOKUP

(

H3

,

B4:E13

,

4

,

FALSE

)

// email address

VLOOKUP only looks right

VLOOKUP can only look to the right. The data you want to retrieve (result values) can appear in any column to the right of the lookup values:

If you need to lookup values to the left, see INDEX and MATCH, or XLOOKUP.

Exact and approximate matching

VLOOKUP has two modes of matching, exact and approximate. The name of the argument that controls matching is “range_lookup“. This is a confusing name, because it seems to have something to do with cell ranges like A1:A10. Actually, the word “range” in this case refers to “range of values” – when range_lookup is TRUE, VLOOKUP will match a range of values rather than an exact value. A good example of this is using VLOOKUP to calculate grades.

It is important to understand that range_lookup defaults to TRUE, which means VLOOKUP will use approximate matching by default, which can be dangerous. Set range_lookup to FALSE to force exact matching:

=

VLOOKUP

(

value

,

table

,

col_index

)

// approximate match (default)

=

VLOOKUP

(

value

,

table

,

col_index

,

TRUE

)

// approximate match

=

VLOOKUP

(

value

,

table

,

col_index

,

FALSE

)

// exact match

Note: You can also supply zero (0) instead of FALSE for an exact match.

Exact match

In most cases, you’ll probably want to use VLOOKUP in exact match mode. This makes sense when you have a unique key to use as a lookup value, for example, the movie title in this data:

The formula in H6 to find Year, based on an exact match of movie title, is:

=

VLOOKUP

(

H4

,

B5:E9

,

2

,

FALSE

)

// FALSE = exact match

Approximate match

In cases when you want the best match, not necessarily an exact match, you’ll want to use approximate mode. For example, below we want to look up a commission rate in the table G5:H10. The lookup values come from column C. In this example, we need to use VLOOKUP in approximate match mode, because in most cases an exact match will never be found. The VLOOKUP formula in D5 is configured to perform an approximate match by setting the last argument to TRUE:

=

VLOOKUP

(

C5

,

\$G\$5:\$H\$10

,

2

,

TRUE

)

// TRUE = approximate match

VLOOKUP will scan values in column G for the lookup value. If an exact match is found, VLOOKUP will use it. If not, VLOOKUP will “step back” and match the previous row.

Note: data must be sorted in ascending order by lookup value when you use approximate match mode with VLOOKUP.

First match

=

VLOOKUP

(

E5

,

B5:C11

,

2

,

FALSE

)

// returns 17

Wildcard match

The VLOOKUP function supports wildcards, which makes it possible to perform a partial match on a lookup value. For instance, you can use VLOOKUP to retrieve values from a table after typing in only part of a lookup value. To use wildcards with VLOOKUP, you must specify the exact match mode by providing FALSE or 0 for the last argument, range_lookup. The formula in H7 retrieves the first name, “Michael”, after typing “Aya” into cell H4:

=

VLOOKUP

(

\$H\$4

&

"*"

,

\$B\$5:\$E\$104

,

2

,

FALSE

)

Read a more detailed explanation here.

Two-way lookup

Inside the VLOOKUP function, the column index argument is normally hard-coded as a static number.  However, you can also create a dynamic column index by using the MATCH function to locate the right column. This technique allows you to create a dynamic two-way lookup, matching on both rows and columns. In the screen below, VLOOKUP is configured to perform a lookup based on Name and Month. The formula in H6 is:

=

VLOOKUP

(

H4

,

B5:E13

,

MATCH

(

H5

,

B4:E4

,

0

),

0

)

For more details, see this example.

Note: In general, INDEX and MATCH is a more flexible way to perform two-way lookups.

Multiple criteria

The VLOOKUP function does not handle multiple criteria natively. However, you can use a helper column to join multiple fields together, and use these fields like multiple criteria inside VLOOKUP.  In the example below, Column B is a helper column that concatenates first and last names together with this formula:

=

C5

&

D5

// helper column

VLOOKUP is configured to do the same thing to create a lookup value. The formula in H6 is:

=

VLOOKUP

(

H4

&

H5

,

B5:E13

,

4

,

0

)

For details, see this example.

Note: INDEX and MATCH and XLOOKUP are more robust ways to handle lookups based on multiple criteria.

VLOOKUP and #N/A errors

If you use VLOOKUP you will inevitably run into the #N/A error. The #N/A error just means “not found”. For example, in the screen below, the lookup value ”Toy Story 2″ does not exist in the lookup table, and all three VLOOKUP formulas return #N/A:

One way to “trap” the NA error is to use the IFNA function like this:

The formula in H6 is:

=

IFNA

(

VLOOKUP

(

H4

,

B5:E9

,

2

,

FALSE

),

"Not found"

)

The message can be customized as desired. To return nothing (i.e. to display a blank result) when VLOOKUP returns #N/A you can use an empty string like this:

=

IFNA

(

VLOOKUP

(

H4

,

B5:E9

,

2

,

FALSE

),

""

)

// no message

The #N/A error is useful because it tells you something is wrong.  In practice, there are many reasons why you might see this error, including:

The lookup value does not exist in the table

The lookup value is misspelled, or contains extra space

Match mode is exact, but should be approximate

The table range is not entered correctly

You are copying VLOOKUP, and the table reference is not locked

Read more: VLOOKUP without #N/A errors

More about VLOOKUP

Other notes

Range_lookup controls whether value needs to match exactly or not. The default is TRUE = allow non-exact match.

Set range_lookup to FALSE to require an exact match and TRUE to allow a non-exact match.

If range_lookup is TRUE (the default setting), a non-exact match will cause the VLOOKUP function to match the nearest value in the table that is still less than value.

When range_lookup is omitted, the VLOOKUP function will allow a non-exact match, but it will use an exact match if one exists.

If range_lookup is TRUE (the default setting) make sure that lookup values in the first row of the table are sorted in ascending order. Otherwise, VLOOKUP may return an incorrect or unexpected value.

If range_lookup is FALSE (require exact match), values in the first column of table do not need to be sorted.

## How To Use The Excel Timevalue Function

Sometimes, times in Excel appear as text values that are not recognized properly as time. The TIMEVALUE function is meant to parse a time that appears as a text value into a valid Excel time. A native Excel time is more useful than text because it is a numeric value that can be formatted as time and directly manipulated in a formula.

The TIMEVALUE function takes just one argument, called time_text. If time_text is a cell address, the value in the cell must be text. If time_text is entered directly into the formula it must be enclosed in double quotes (“”). Time_text should be supplied in a text format that Excel can recognize, for example, “6:45 PM” or “18:45”. TIMEVALUE ignores dates if present in a text string.

The TIMEVALUE function creates a time in serial number format from a date and/or time in an Excel text format. TIMEVALUE will return a decimal number between 0 and 0.99988426, representing 12:00:00 AM to 11:59:59 PM. Because the maximum value returned by TIMEVALUE is less than 1, hours will reset every 24 hours (like a clock).

Examples

The formulas below show the output from TIMEVALUE:

=

TIMEVALUE

(

"12:00"

)

// returns 0.5

=

TIMEVALUE

(

"12:00 PM"

)

// returns 0.5

=

TIMEVALUE

(

"18:00"

)

// returns 0.75

To display the output from TIMEVALUE as a formatted time, apply a time number format.

Alternative formula

Notice that the TIMEVALUE formula in C15 fails with a #VALUE! error, because cell B15 already contains a valid time. This is a limitation of the TIMEVALUE function. If you have a mix of valid and invalid dates, you can use the simple formula below as an alternative:

=

A1

+

0

The math operation of adding zero will cause Excel will try to coerce the value in A1 to a number. If Excel is able parse the text into a proper time it will return a valid time as a decimal number. If the time is already a valid Excel time, adding zero will have no effect, and generate no error.

Notes

TIMEVALUE will return a #VALUE error if time_text does not contain time formatted as text.

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