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Question about Texas Instruments TI-86 Calculator

# Trigonometric functions how do i get the cosecant measure in radians?

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### courouge

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Put the calculator in radian mode. Find the sine of the angle (sin(angle)), invert the result (1/x or x^(-1)). csc = 1 / sin

Posted on Oct 05, 2007

### Anonymous

Put the calculator in radian mode. Find the sine of the angle (sin(angle)), invert the result (1/x or x^(-1)). csc = 1 / sin

Posted on Sep 29, 2008

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It means your calculator is currently set to measure angles in degrees.

There are three common units to measure angles. A full circle is 360 degrees, or 400 grads, or two pi radians. The results of the trigonometric functions depend on the current measure, just as you'd get different numbers if you measure a person's height in inches, feet, or meters.

### I'm trying to graph in radians on a casio fx-9750ga plus, but it doesn't show up on my screen. what should i do?

To get results in radians you must configure the angle unit to be degree.
1. In Run screen press [SHIFT][MENU] to access (SETUP).
2. Use Down arrow to highlight the line Angle :
3. Press F2 key to select the TAB Radian.
4. Once you do that all values (input of trigonometric functions and polar graph functions OR output of inverse trigonometric functions) are in radians.
If your function is periodic (and all trigonometric functions are) set the window dimensions Xmin
= negative (2 or 3)P and Xmax) = (2 or 3) PI. Adjust if necessary to a smaller domain.

To get results in radians you must configure the angle unit to be degree.
1. In Run screen press [SHIFT][MENU] to access (SETUP).
2. Use Down arrow to highlight the line Angle :
3. Press F2 key to select the TAB Radian.
4. Once you do that all values (input of trigonometric functions and polar graph functions OR output of inverse trigonometric functions) are in radians.
However I believe I sense a misconception in your request. You can press [SHIFT][x10^X] to enter PI, but the calculator will never give you an angle result as a fraction of PI. You will have the numerical approximation of it that corresponds to the number of decimal digits you are keeping.

### Some of my class set of Ti - 84 silver aren't computing sine and cosine correctly. I've tried clearing RAM and looked at settings. Please help!

I have answered many questions asked by teachers and professors, and very few, if any, deigned to rate the posts. Why do I set myself up for yet another disappointment: I just like to help.

Anyway, the most common source of errors with computation of trigonometric functions is the angle unit. On Ti 83/84Plus (SE) calculators there are two angle units: the degree and the radian.

To verify which angle unit is set as default on a calculator, press MODE. You will see the following screen. The relevant line is the 3rd. On the screen RADIAN is highlighted, meaning that all angle values you feed to trigonometric functions are interpreted as radian measures.
Similarly, all values returned by inverse trigonometric functions are in radians.

I do not know what grades you teach, but if you are doing any differential calculus, the only appropriate unit is the radian. Only for the radian unit is the derivative of sin(x) equal to -cos(x). For the degree, you must introduce a factor to adjust (as a change of variable).

Set all your calculators to use the angle unit you are using in your teaching, and there will be no unexpected results.

### How do I put cosecant, secant, and cotangent functions into my ti-84 plus?

By definition
1. cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
2. secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
3. cotangent of X =1/tan(X), must not be confused with arc tangent [tan^-1]
Because of these simple relations, calculator makers do not implement them with specific key sequences.
On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees
1. You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
2. You enter [sin] [ ) ] 37 [ENTER] followed by [X^-1] to take the reciprocal of the previous answer. The [X^-1] key is the one just below [MATH].
A word of caution: secant cosecant and cotangent must not be confused with the inverse trigonometric functions arcsin, arccos, arctan

### I have a SHARP EL-501W calculator and i am getting the wrong answers with the tan -1 function

Hi,
The source of errors is most certainly due to the wrong schoice of angle unit (degree or radian). If the default angle unit set in your calculator is the degree, any value fed to the trigonometric functions (sin, cos, tan) is considered to be expressed in degrees. Consequently, if you calculate the arctangent ( tan^-1) of a value, the angle returend by that inverse trigonometric function is expressed implicitly in degrees.

Similarly if radian is the default angle unit in your calculator, any angle returned by an inverse trigonometric function (arcos, arcsin, arctan) is in radian.

Set the default angle unit as the one required by your problem at hand. This way, the angles returned will be in the right unit and you will not have a problem of interpretation.

Hope it helps.

### I am getting the wrong answers with the tan -1 function

Hello,
That habit of TI, Casio, and Sharp to label the inverse trigonometric functions with the -1 superscript can cause confusions.
1. The inverse trigonometric functions arcosine, arcsine, and arctangent (labeled by manufacturers as cos^-1, sin^-1, and tan^-1) should not be confused with the other trigonometric functions known as secant(x) =1/cos(x), cosecant(x)=1/sin(x) and cotangent(x) = 1/tan(x).
2. To avoid errors in the use of the inverse trigonometric functions, one must be careful and set the angle unit to the one required by the problem at hand (degrees, or radians)
3. To make the trigonometric functions really functions, their range is restricted.
4. In this calculator arcosine (x) gives results between 0 and 180 degrees (if angle MODE is Degree) or between 0 and Pi radians (if angle MODE is Radian).
5. The range of results for arcsine(x) and arctangent(x) is between -90 degrees and +90 degrees (if angle MODE Degree) or -Pi/2 and Pi/2 (if angle MODE is Radian)
With this information you should be able to set the angle unit correctly ([MODE][Radian] or [MODE][Degree] ) and interpret the results. If you want to extend the angle to other values, use the periodicity of the trigonometric functions.

Hope it helps

### How to use trig function keys on my casio fx-300ES

Hello,
You have 3 keys for the main trigonometric functions: [SIN], [COS] and [TAN]
To use them correctly you must set the angle unit to the one your problem calls for.
Press [SIFT][MODE] [3:Deg] for degree, [4:Rad] for radian, [5:Grad] for grad. Dependig on angle unit chosen a small D, R, or G appears on the top of the screen.

If you need the inverse trigonometric functions arcsine, arccosine, arctangent, you access them by first pressing the [SHIFT] key
Thus
arcsine [SHIFT][SIN] (sin^-1)
arcosine [SHIFT][COS] (cos^-1)
arctangent [SHIFT][TAN] (tan^-1)

The syntax for the function is
[SIN] # [ ) ] [=]; [SIN] 30 [ ) ] [=] gives 0.5
[COS] # [ ) ] [=] [COS] 19 [ ) ] [=] gives 0.945518576

Note: if the argument of the functions are numbers, the right parenthesis is not necessary. But if the argument is an expression (with various operations) better put the parenthesis to make sure the calculator is performing as one wants it to.

By the way, there are no keys, or key combinations to calculate cotangent, cosecant, and secant, but you can use the definitions:

cotangent (x) = 1/tan(x) Do not confuse it with tan^-1
cosecant(x) = 1/sin(x) Do not confuse it with sin^-1
secant(x) = 1/cos(x) Do not confuse it with cos^-1

Hope it helps.
Oct 30, 2009 • Casio fx-300ES Calculator

### Need to know how to obtain the cot,csc, and see in the degree mode and radian mode

Hello,
There are no dedicated keys for these trigonometric functions, for the simple reason that they can be obtained from the tan, sin, and cos by a simple division.
cotangent (x) =1/tan(x) . Do not confuse with the arc tangent tan^(-1)
cosecant (x) = 1/sin(x) . Do not confuse with the arcsine sin^(-1)
secant(x) =1/cos(x) Do not confuse with the arccosine cos^(-10)

If you know how to use the tan, cos, and sin, with angle unit in degrees or radians, then there will not be any problem

If angle unit is degree, any number you give a trigonometric function is interpreted as degree. For instance if mode is in degree , and you calculate cos(PI) do not expect the value -1. You will have the value corresponding to the cosine of of 3.14159 degrees, namely 0.99849715

Now for you if you are interested.
If [MODE] is in degrees you can still enter angles in radians
You use the [2nd][ANGLE] [3: raised r] [ENTeR].
Here is a screen capture to show you more clearly.

The raised r is obtained by [2nd][ANGLE][3: raised r] [ENTER]

Hope it helps.

### Cosecant

Hello,
The cosecant function is defined by
cosec(x) = 1/sin(x)

1[/] [sin] x.
Do not confuse this function with the arcsine function which is accessed by [2nd][sin to the -1]. When you use trigonometric functions make sure that the angle unit (Rad, dgree, grad) is the one you want.

Hope it helps.

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