Use your graphing calculator to graph
y = cos^−1(x)in degree mode. Use the graph with the appropriate command to evaluate each expression.
(a)cos^−1(√2/2)
= ___________˚
(b)cos^−1(-1/2)
= _____________°
(c)arccos (√3/2)
= _____________˚
What is arccos?
How do I solve these using the graph? I put it in my calculator but the graph did not show up :/
arccos is the inverse cosine.
If x = cos(y) then y = arccos(x)
Mosey on over to
http://rechneronline.de/function-graphs/
and enter arccos(x) for the function. Then set the x and y ranges from -1 to 1 and draw the graph. You can then get a feel for the y values needed. They will be in radians, however. If you want to read them off in degrees, enter
arccos(x) * 180/pi
and set the y range from 0 to 180
As a check, remember that
cos pi/4 = √2/2
cos 2pi/3 = -1/2
cos pi/6 = √3/2
To graph the function y = cos^−1(x) (inverse cosine) in degree mode, you can follow these steps using a graphing calculator:
1. Turn on your graphing calculator.
2. Set your calculator to degree mode. This setting can usually be found in the "Mode" menu, where you can switch between degree and radian modes. Make sure to select degree mode for this specific problem.
3. Enter the equation y = cos^-1(x) into the calculator. The ^ symbol denotes exponentiation or power.
4. Press the graph or plot button to display the graph on the screen.
Now let's solve the expressions using the graph:
(a) To evaluate cos^−1(√2/2), you need to find the x-coordinate on the graph where the y-coordinate is √2/2. Since the function y = cos^−1(x) represents the inverse of the cosine function, the x-coordinate will represent the angle in degrees where the cosine is equal to √2/2.
(b) For cos^−1(-1/2), you need to find the x-coordinate on the graph where the y-coordinate is -1/2. Again, this x-coordinate will represent the angle in degrees where the cosine is equal to -1/2.
(c) Lastly, for arccos (√3/2), you can directly use the cosine function. Since the inverse cosine function (cos^−1) is the exact same function as arccos, you can plug in √3/2 into the cosine function to find the angle in degrees.
If the graph did not show up on your calculator, please make sure you have followed the steps correctly and that there are no errors in the equation you entered. If you are still having difficulties, consult the user manual for your specific graphing calculator or try resetting your calculator to default settings.