How do you find: cot(-5pie/4)?
you have to know that cotx = 1/tanx
so you could just trustfully change your calculator to radians
enter 5*pi/4, press =, press +/-,
then press Tan, =, then the 1/x key
you should get -1
or...
you could do it the more rewarding way without a calculator.
pi/4 radians is 45º, so 5pi/4 is 225º
-225º is a clockwise rotation and lands you in the second quadrant where the tan is negative, and 45º up from the x-axis.
now tan45º=1, so tan(-225º)=-1
then cot(-225)=1/-1=-1
thanks.
Ah, finding cot(-5pi/4. Quite the mathematical adventure, isn't it?
Well, if we want to find cot(-5pi/4), we can start by remembering that cot(x) is the inverse of tan(x), so we can use the relationship cot(x) = 1/tan(x).
Now, you can certainly trust your trusty calculator to do this calculation for you. Just enter -5pi/4, hit the = button, then the +/- button to account for the negative sign. After that, press the Tan button, followed by the 1/x button, and voila! Your answer should be -1.
But, if you're feeling particularly adventurous and want to flex those brain muscles, you can also find the answer without a calculator. Here's how:
First, let's convert -5pi/4 to degrees. Pi/4 radians is equal to 45 degrees, so -5pi/4 radians would be -225 degrees in standard form.
Now, -225 degrees is in the second quadrant, where the tan function is negative. Also, if you imagine going 45 degrees up from the x-axis, you'll land at -225 degrees.
Since tan(45 degrees) = 1, we can conclude that tan(-225 degrees) = -1.
And since cot(x) is the inverse of tan(x), cot(-225 degrees) = 1/-1, which simplifies to -1.
So, whether you choose the calculator route or the adventurous route, the answer is indeed -1. Happy mathematical travels!