Videos > Example: Calculator to evaluate inverse trig function
Example: Calculator to evaluate inverse trig function Video Lecture
FAQs on Example: Calculator to evaluate inverse trig function Video Lecture
| 1. How do I calculate the inverse trig function of a given value? |  |
Ans. To calculate the inverse trig function of a value, you can use the inverse trigonometric functions on a calculator. Simply input the value and select the appropriate inverse trig function (e.g., arcsin, arccos, arctan) to obtain the angle or measurement.
| 2. What is the importance of inverse trig functions in mathematics? | |
Ans. Inverse trig functions are essential in solving trigonometric equations, as they allow us to find the angle or measurement given a certain trigonometric value. They are also used in various branches of mathematics, physics, and engineering to solve real-world problems involving angles, distances, and vectors.
| 3. Can I use a regular calculator to evaluate inverse trig functions? | |
Ans. Yes, most scientific or graphing calculators have the inverse trig functions built-in. Look for the buttons labeled "sin⁻¹" (arcsin), "cos⁻¹" (arccos), and "tan⁻¹" (arctan) on your calculator. If you are using a basic calculator, you may need to consult a table of inverse trig functions.
| 4. Are there any restrictions or limitations when using inverse trig functions? | |
Ans. Yes, there are certain restrictions when using inverse trig functions. For example, the domain of arcsin and arccos is limited to [-1, 1], while the domain of arctan is unrestricted. Additionally, be aware of the principal value of the inverse trig functions, which is typically within a specific range for each function.
| 5. Can I use the inverse trig functions to solve right-angled triangles? | |
Ans. Yes, inverse trig functions are often used to solve right-angled triangles. By knowing the lengths of two sides of a right triangle, you can apply the appropriate inverse trig function (e.g., arcsin, arccos, arctan) to find the angle measures. This is especially useful in trigonometry and geometry problems involving triangles.
Text Transcript from Video
Use your calculator to find
the angle to the nearest
degree, whose tangent
value is 0.875.
So what do you think
that's going to be?
The angle to the nearest degree,
whose tangent value is 0.875.
Well, the first thing
is to be careful.
They are not asking for
the tangent of 0.875.
They're not saying
that 0.875 is an angle
and we want to find
the tangent of it.
That is not what they're asking.
They're asking
something different.
They're saying that
there's some angle.
Maybe we could call it theta.
There's some angle
that if we were
to take the tangent
of that angle,
then we are going to get 0.875.
So how do we figure
out this mystery angle
using our calculator?
Well, the way we
do it is a function
called the inverse
tangent function.
Or sometimes it's called
the arc tangent function.
And essentially,
if you apply that,
and if you just view
this as an equation,
you take the inverse
tangent of something.
So if you take the
inverse tangent of this.
And you take the
inverse tangent--
let me clear this
out a little bit.
I'm just taking the inverse
tangent of both sides.
0.875.
On the left hand side you're
just left with the angle.
The inverse tangent of tangent
is just your original angle.
And on the right hand side
you get the inverse tangent
of 0.875.
And if you're in
degree mode this
is going to return
an angle in degrees.
And if you're in radians
mode it will return angle
in terms of radians.
But let's figure this out
using our calculators.
So we could use the
traditional calculator,
or more traditional calculator.
Let me clear everything out.
Now all I see is a tangent.
I don't see the inverse tangent.
In order to get that you have
to press the inverse button
right over here.
And this is not the
reciprocal button.
This is the reciprocal button.
This right over
here is the inverse
to get the inverse functions.
So you press inverse and notice
you saw that this changed.
This would not actually happened
on an actual calculator.
But you get the idea.
The actual calculator might
have something up here
to show that you can
access it that way.
And so now we could say 0.875.
And we're going to take
the inverse tangent of it.
Inverse tangent.
So take the inverse
tangent of it.
We already know that
we're in degree mode.
And we want to round
to the nearest degree.
So it's going to be, if we
round to the nearest degree--
we get 41 degrees.
So theta is approximately,
it's not exactly--
we're rounding-- 41 degrees.
Let's do the exact same thing
with the graphing calculator.
So let me turn it on.
And let me clear it.
And now we want to take
the inverse tangent.
If you have this calculator it
will look exactly like this.
You see this tangent.
Inverse tangent.
Tan.
They have it written as
to the negative 1 power.
It looks like that.
But it's not really to
the negative 1 power.
It's really inverse tangent.
It's right there in yellow.
To access that you press
second and then that function.
Inverse tangent of 0.875.
We get the exact same value.
It's roughly equal
to 41 degrees if we
round to the nearest degree.
the angle to the nearest
degree, whose tangent
value is 0.875.
So what do you think
that's going to be?
The angle to the nearest degree,
whose tangent value is 0.875.
Well, the first thing
is to be careful.
They are not asking for
the tangent of 0.875.
They're not saying
that 0.875 is an angle
and we want to find
the tangent of it.
That is not what they're asking.
They're asking
something different.
They're saying that
there's some angle.
Maybe we could call it theta.
There's some angle
that if we were
to take the tangent
of that angle,
then we are going to get 0.875.
So how do we figure
out this mystery angle
using our calculator?
Well, the way we
do it is a function
called the inverse
tangent function.
Or sometimes it's called
the arc tangent function.
And essentially,
if you apply that,
and if you just view
this as an equation,
you take the inverse
tangent of something.
So if you take the
inverse tangent of this.
And you take the
inverse tangent--
let me clear this
out a little bit.
I'm just taking the inverse
tangent of both sides.
0.875.
On the left hand side you're
just left with the angle.
The inverse tangent of tangent
is just your original angle.
And on the right hand side
you get the inverse tangent
of 0.875.
And if you're in
degree mode this
is going to return
an angle in degrees.
And if you're in radians
mode it will return angle
in terms of radians.
But let's figure this out
using our calculators.
So we could use the
traditional calculator,
or more traditional calculator.
Let me clear everything out.
Now all I see is a tangent.
I don't see the inverse tangent.
In order to get that you have
to press the inverse button
right over here.
And this is not the
reciprocal button.
This is the reciprocal button.
This right over
here is the inverse
to get the inverse functions.
So you press inverse and notice
you saw that this changed.
This would not actually happened
on an actual calculator.
But you get the idea.
The actual calculator might
have something up here
to show that you can
access it that way.
And so now we could say 0.875.
And we're going to take
the inverse tangent of it.
Inverse tangent.
So take the inverse
tangent of it.
We already know that
we're in degree mode.
And we want to round
to the nearest degree.
So it's going to be, if we
round to the nearest degree--
we get 41 degrees.
So theta is approximately,
it's not exactly--
we're rounding-- 41 degrees.
Let's do the exact same thing
with the graphing calculator.
So let me turn it on.
And let me clear it.
And now we want to take
the inverse tangent.
If you have this calculator it
will look exactly like this.
You see this tangent.
Inverse tangent.
Tan.
They have it written as
to the negative 1 power.
It looks like that.
But it's not really to
the negative 1 power.
It's really inverse tangent.
It's right there in yellow.
To access that you press
second and then that function.
Inverse tangent of 0.875.
We get the exact same value.
It's roughly equal
to 41 degrees if we
round to the nearest degree.
About this Video
Oct 07, 2025
Last updated
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