This lesson we'll cover how to evaluate the
given expressions using a free online graphing calculator.
And there are some notes here on the right for reference
that you may find helpful.
It is important to recognize the calculator
is always in radian mode,
if you have an expression that uses degrees,
you would have to convert to radians.
Let's go ahead and open up the calculator
by clicking on the link below
and then we'll evaluate the expressions.
The calculator does have quite a few features
because we are evaluating expressions,
we will only be using the lower left-hand corner
of the screen.
We enter the expressions from the keyboard
into the cell below that's labeled to type an expression.
So let's go ahead adjust the windows so we can see
the expressions as well as the calculator.
The first expression is two plus three times five.
We click in the type an expression cell
and enter two plus three.
The multiplication symbol is above the eight,
and therefore we press Shift + eight for multiplication,
then five and then click Enter,
the expression is equal to 17.
Next we have the expression negative four times the quantity
seven minus 15 squared plus 82.
We click in the expression cell,
enter negative four, open parenthesis, seven minus 15,
close parenthesis, to enter the exponent of two,
we need to caret our exponent key, which is above the six.
We press Shift + six for the exponent key or caret,
and then we enter the exponent of two
and then plus 82, and Enter.
Notice how the calculator does show
how the entry is interpreted.
So it's always important to check this
to make sure it matches the original expression.
The expression is equal to negative 174.
Next we have the square to 49.
To enter a square root,
we type S-Q-R-T and then we enter
the radicand and parentheses,
so we have open parenthesis 49, close parenthesis, Enter.
The square root of 49 is equal to seven.
Next we have 16 raise to the power of three fourths.
For this expression,
we do need parentheses around the exponent,
so the entire fraction is in the position of the exponent.
Clicking in the expression cell, we enter the base of 16,
then the exponent key or caret which is Shift + six,
open parenthesis, three divided by four, close parenthesis.
Notice how the parentheses indicate
three fourths is the exponent on 16.
If we click enter,
we can also see here that the exponent is three fourths,
and the expression is equal to eight.
A very common mistake is to enter 16
exponent three divided by four.
But in this case, the exponent of 16 is three,
and then the expression is divided by four,
which we can see if we click Enter.
So this is not the correct expression,
but that's why it's important to check
how the calculator interprets the entry.
We now know 16 to the three fourths power is equal to eight.
Next we have the cube root of 27.
Whenever we have a radical where the index
is three or higher,
we use different notation for the entry.
We enter root, R-O-O-T,
and then we enter the index in parentheses.
For a cube root,
the index is three so we enter a three in parentheses.
And then we enter the radican of 27
in another set of parentheses.
This is how we evaluate the cube root of 27
which we can see is equal to three.
Next we have the absolute value of negative seven.
To enter an absolute value, we type A-B-S
and then open parenthesis, negative seven,
close parenthesis and Enter.
The absolute value of negative seven is seven.
Next we have three cosine pi plus two
natural log of e cubed.
Clicking in the expression cell,
we enter three cosine, open parenthesis for pi we enter P-I,
close parenthesis plus two, for natural log, we type in ln,
open parenthesis e.
Once again we need the exponent key or caret
which is Shift + six.
Three close parenthesis and Enter.
We can see on the left we entered the expression correctly,
and the expression is equal to three.
Next we have inverse sine or arc sine of
the square with three divided by two.
We can enter this two ways,
entering in just like it looks we have sine,
the exponent key or a caret, negative one,
open parenthesis, S-Q-R-T, open parenthesis three,
close parenthesis divided by two,
close parenthesis and Enter.
So one thing to recognize here
is the exact value here is pi divided by three radians,
but the calculator will only give us
a decimal approximation.
Instead of using inverse sine notation,
we can also use arc sine,
and of course get the same result.
The last expression is log base two of eight plus pi.
So we go to the calculator and enter log,
if we don't indicate a base,
and it's common log or log base 10,
here we have base two.
So to enter the base of two, we click underscore,
which is Shift + dash, two and then open parenthesis,
eight close parenthesis.
So if a log has any base other than e or 10,
we use this notation here.
Again, if it's log base 10, we just leave off the base.
So we have log_2 open parenthesis, eight,
close parenthesis and then plus pi, and Enter.
So those are all the expressions.
But I do want to show you one more quick thing
about the calculator.
You can find in these notes as well as other help
under the Help menu
by clicking in the Help link in the upper right-hand corner.
So you may want to review this reference.
I hope you found this helpful.