Question about Texas Instruments TI-30XA Calculator

# How do you find arc sin on this calculator - Texas Instruments TI-30XA Calculator

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Hi,
Before using the inverse trigonometric functions, make sure your calculator has the right unit as angle unit. The unit of the values returned by the inverse trigonometric functions is the same as the default angle unit. This being said, you access the arcsine function by pressing 2nd sin^-1
The syntax is as follows number 2nd sin^-1 =

Hope it helps.
Thank you for rating the solution.

Posted on Dec 09, 2009

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Posted on Jan 02, 2017

The sine of 6pi is indeed zero. The calculator works with twelve decimal digits while pi is an irrational number with an infinite number of decimal digits. Thus the calculator cannot actually calculate the sine of 6pi, instead it calculates the sine of 18.8495559215. The sine of that number is close to zero but not quite, about 0.000000000002 which is what the calculator shows. This is a natural consequence of using finite machines to deal with infinite numbers.

In degrees, 3*360 is 1080 exactly and thus the calculator can produce an answer of exactly zero.

You'll notice that the calculator also gives a nonzero result for the sine of 4pi.

The "proper" fix for this is something called "argument reduction." If the argument lies outside the range of 0 to 2pi (or alternatively, the range -pi to pi), add or subtract multiples of 2pi until the argument is inside the range. So in this case, subtract 6pi from 6pi to get zero, then take the sine of that.

Bear in mind that argument reduction won't always work, since it too is limited to twelve-digit arithmetic.

Posted on Dec 12, 2010

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## Related Questions:

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It's arcus sinus, which, as opposed to the sinus function, returns the angle.
For example:
sin 30 = 1/2
arc sin 1/2 = 30 deg.

Arc sin, arc cos, atan actg are often referred to sin-1, cos-1 tan-1 ctg-1.

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### When ever i press sin^-1, and type in a number, the answer is always "domain error" on my ti 30x iis, how can I fix this problem?

Not quite true. (Explanation at the end)
The sine and cosine of an angle have values in the closed interval [-1,1]. That means whatever the value of the angle, its sine or its cosine cannot be less than -1 or greater than 1.
When you consider the inverse problem where you want to find the angle whose sine or cosine is known, you must take the values of the sine or cosine in the interval [-1,1]. That is the domain of the functions arc sine and arc cosine. So if you take a value outside the domain [-1,1], and want to calculate the angle to which it belongs, the calculator signals that there a domain error, because there is no angle that answers the question. Limit the arguments of the sin^-1 and cos^-1 to values in [-1,1]
For the inverses of arc tangent and arc cotangent functions there is no domain limitation because the range of tangent and cotangent is the whole real line ]-infinity, +infinity[.

Mar 30, 2014 | Office Equipment & Supplies

### My TI-30XB WONT CALCULATE INVERSE COS OR INVERSE SIN

Does it refuse to do so or does it give an error message?
Three common errors:
1. Not having the correct angle unit. Wrong result, No error message
2. Confusing reciprocal of sine (1/sin(x) with arc sine (x) ,sin^-1(x). Confusing the reciprocal of cosine, 1/cos(x) with arc cosine (cos^-1(x)). Wrong result, No error message
3. Taking the argument of the inverse sine and/or inverse cosine functions outside the interval [-1,1]. This gives a domain error.

Oct 28, 2013 | Texas Instruments TI-81 Calculator

### How do i put arc on the calculator

For the inverse trig functions, press 2ND then the trig function key. For example, to calculate the arcsine of 0.5, press 2ND SIN . 5 ENTER

Oct 18, 2013 | Texas Instruments TI-83 Plus Calculator

### I can not find the arc key or the INV key

The INV key that you may find on some scientific calculators has, on the TI 83/84/ Plus calculators, an equivalent key marked [2nd].

On the TI83/84 Plus, each trigonometric function has a second marking [SIN^-1], [COS^-1] or [TAN^-1]. To calculate the inverses of trigonometric functions ( arc sine, arc cosine, arc tangent) you press [2nd] followed by the relevant trigonometric function key For example, [2nd] [SIN] displays sin^-1( on the command line.

Unfortunately the hyperbolic functions and their inverses are only accessed through the CATALOG. You press [2nd][0] to open the CATALOG. Then you scroll down the CATALOG list to reach cosh(, cosh^-(, sinh(, sinh^-1(, tanh(, or tanh^-1(.
To speed the search in the catalog, you use the ALPHA keyboard: To reach cosh(, press[PRGM] and you scroll down from there.

Feb 27, 2012 | Texas Instruments TI-84 Plus Calculator

### Error when using inverse trig inever used to get these errors when trying to find angles using whole numbers inside the inverse trig functions but now it will only calculate SOME fractions. wether the...

If you are trying to calculate arcsine (sin^-1) and arccosine (cos^-1) the only whole number you can use are -1,0 and 1. This due to the fact that the domain of these functions is the closed interval [-1,1]. Any value outside that interval will trigger an error message. No limitation on the argument of the arc tangent or arc cotangent functions

If the angle unit is set to degree the arc will be in degrees, and if angle unit is radian, the arc will be in radians.

Sep 27, 2011 | Texas Instruments TI-84 Plus Calculator

### Cant find the arc or inverse button

The trigonometric function [SIN],[COS] and [TAN] have inverse functions arc-sine, arc-cosine, and arc-tangent which are also implemented on scientific calculators. To access the inverse trigonometric functions you use the sequences [SHIFT][SIN], [SHIFT][COS] and [SHIFT][TAN]. The functions are marked on the body of the calculator as [SIN^-1], [COS^-1] and [TAN^-1].
When you use these functions, make sure that the angle unit is correctly set (as required by the problem you are solving) because the angle values returned are in the same unit as the one set.

Jan 15, 2011 | Casio FX-115ES Scientific Calculator

### I get err:domain on my TI-84 plus when i do Sin -1 (60) why?

While the domain of the sine function is the whole of the real line, it range spans the interval [-1,1]. In other words the sine of an arbitrary angle is imperatively somewhere in the closed interval [-1,1].
So when you want to find the arc sine corresponding to a given value of a sine function, you cannot give as argument to the arc sine [sin^-1] a value that lies outside the interval [-1,1].

For your case, the argument is 60 and it is outside the permitted domain [-1,1]. That is why the calculator protests by signaling a domain error.

Oct 28, 2010 | Texas Instruments TI-84 Plus Calculator

### 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

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

### TI-84 Plus silver edition sin/cos/tan

for function = (sin,cos,tan,sec,cosec,cotan)
arc(function) = function^-1, calculated in the first quadrant for simplicity(0-pi/2) (0-90deg), as all functions repeat circularly
just another method of notation

http://www.mathwords.com/t/tangent_inverse.htm

Jun 19, 2008 | Texas Instruments TI-84 Plus Silver...

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