Question about Texas Instruments TI-86 Calculator

Re: trigonometric functions

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

Re: trigonometric functions

Posted on Sep 29, 2008

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.

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.

Jul 15, 2014 | Texas Instruments TI 30XIIS Scientific...

To get results in radians you must configure the angle unit to be degree.

- In Run screen press [SHIFT][MENU] to access (SETUP).
- Use Down arrow to highlight the line Angle :
- Press F2 key to select the TAB Radian.
- Once you do that all values (input of trigonometric functions and polar graph functions OR output of inverse trigonometric functions) are in radians.

Sep 09, 2010 | Casio FX-9750GPlus Calculator

To get results in radians you must configure the angle unit to be degree.

- In Run screen press [SHIFT][MENU] to access (SETUP).
- Use Down arrow to highlight the line Angle :
- Press F2 key to select the TAB Radian.
- Once you do that all values (input of trigonometric functions and polar graph functions OR output of inverse trigonometric functions) are in radians.

Sep 09, 2010 | Casio FX-9750GPlus Calculator

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.

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.

Mar 09, 2010 | Texas Instruments TI-84 Plus Silver...

By definition

On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees

- cosecant of X =1/sin(X), must not be confused with arc sine [sin^-1]
- secant of X =1/cos(X), must not be confused with arc cosine [cos^-1]
- cotangent of X =1/tan(X), must not be confused with arc tangent [tan^-1]

On this calculator, you have two ways to calculate one of these functions. EX cosecant of 37 degrees

- You enter 1 / [sin] 37 [ ) ] [ENTER] result is 1.661640141
- 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].

Jan 21, 2010 | Texas Instruments TI-84 Plus Calculator

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.

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.

Dec 07, 2009 | Sharp EL-501WBBL Calculator

Hello,

That habit of TI, Casio, and Sharp to label the inverse trigonometric functions with the -1 superscript can cause confusions.

Hope it helps

That habit of TI, Casio, and Sharp to label the inverse trigonometric functions with the -1 superscript can cause confusions.

- 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).
- 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)
- To make the trigonometric functions really functions, their range is restricted.
- 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).
- 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)

Hope it helps

Nov 06, 2009 | Texas Instruments TI-83 Plus Calculator

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.

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:

Hope it helps.

Oct 30, 2009 | Casio fx-300ES Calculator

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.

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.

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.

Oct 13, 2009 | Texas Instruments TI-83 Plus Calculator

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.

The cosecant function is defined by

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.

Sep 18, 2009 | Texas Instruments TI-30XA Calculator

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