Question about Texas Instruments TI-86 Calculator

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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

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Posted on Sep 29, 2008

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Posted on Jan 02, 2017

Here is some help

180deg is equivalent to Pi radians

Take some angle. Its measure in degrees is say x_deg, Its measure expressed in radians is x_rad.

The fraction of 180 deg that the angle represents is equal to the fraction of PI that this angle represents.

Conclusion: the ratio x_deg/ 180 deg must be equal to the ratio of x_rad/PI

x_deg/180 deg=x_rad/PI

Isolate X-rad in the above equation. Some will tell you to cross multiply.

x_rad=(Pi/180)*x_deg

Application: x_deg=-525 in radians?

x_rad= (PI/180)*(-525)=-(525/180)*PI

Keep the value (525/180) as a fraction reduced to its simplest form. The result is 35/12

180deg is equivalent to Pi radians

Take some angle. Its measure in degrees is say x_deg, Its measure expressed in radians is x_rad.

The fraction of 180 deg that the angle represents is equal to the fraction of PI that this angle represents.

Conclusion: the ratio x_deg/ 180 deg must be equal to the ratio of x_rad/PI

x_deg/180 deg=x_rad/PI

Isolate X-rad in the above equation. Some will tell you to cross multiply.

x_rad=(Pi/180)*x_deg

Application: x_deg=-525 in radians?

x_rad= (PI/180)*(-525)=-(525/180)*PI

Keep the value (525/180) as a fraction reduced to its simplest form. The result is 35/12

Sep 26, 2011 | Casio FX-115ES Scientific Calculator

TWO THINGS YOU NEED TO KNOW, Eli.1. Secant will NEVER return a degree measure (or even a radian measure) no matter what computer or calculator you use. The reason is because secant returns the ratio of sides (hypotenuse over adjacent), which has a range of and find its reciprocal (ie, flip the number upside down: the reciprocal of 5 is one-fifth). That's all.B. TI-84 only uses the three basic trig functions. Secant is the reciprocal of cosine. Therefore, in order to find the secant of -1.2 radians you need to be in Radian mode (see #2 above). From there, you just find the cosine of -1.2 and take that values reciprocal (ie, flip the number upside down: the reciprocal of 10 is point one) . That's all. Math lesson: 1 Radian = 180 Degrees. Therefore, 1.2 Radians is roughly one-third of pi, therefore it is roughly one-third of 180 degrees; therefore -1.2 radians would be nearly -60 degrees (a very friendly angle measure). I hope that helps If not, you should call Texas Instruments because they've got friendly people who are happy to assist anyone. Questions like this are right up their ally, advanced questions like the syntax of the poisson cumulative distribution function are not. So, you're fine. For in depth math help holler at www.THEMATHCHEETAH.comIn Short: Secant returns ratios and NOT degrees or radians. Secant is the reciprocal to cosine. Arcsecant WILL return degrees/radians. Your calculator can be set to either mode.TEXAS INSTRUMENTS >>>>> all calculators ever made.

Mar 08, 2011 | Texas Instruments TI-84 Plus Calculator

There are no keys for cosecant, secant, and cotangent. You can calculate those ratios as

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = 1/tan(x)

Simply calculate the trig ratio on the right and then take its reciprocal.

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = 1/tan(x)

Simply calculate the trig ratio on the right and then take its reciprocal.

Dec 14, 2010 | Texas Instruments TI-83 Plus 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

Alot of people seem to be having this problem. Angles can be measured
in two units, degrees and radians. Your calculator is currently doing
everything in terms of radians. I have an 84 but I'm sure the 83 is
similar, go under MODE and look for Degrees and Radians and make sure
you choose degrees. if you have to convert, 360[degrees] = 2* pi
[radians]

(easy to remember, 360deg in a circle, 2pi radians in a circle)

Good luck

(easy to remember, 360deg in a circle, 2pi radians in a circle)

Good luck

Aug 11, 2009 | Texas Instruments TI-83 Plus Calculator

I shall attempt :D

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

May 12, 2009 | ValuSoft Bible Collection (10281) for PC

reset ur calculator. press 2nd 6 F1 3 Enter. Note that all your data will be gone

Jun 07, 2008 | Texas Instruments TI-89 Calculator

cosec = 1/sin and sec = 1/cos

Oct 03, 2007 | Texas Instruments TI-36 X Solar Calculator

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