Expert: Bobby Soltani - 1/23/2005

Question
I need to check something. When i click cos^-1 on my computer is that giving me the value for Sec, same for the others. In otherwords, does

cos^-1 x = Sec x
sin^-1 x = Csc x
tan^-1 x = Cot

also if i have something like this

cot(x) = -12/5
do i just calculate -12/5, then click tan, since cot(x) and tan(x) are the opposite of each other.

is this correct to say

cot(x) = -12/5
tan(x) = -5/12

then what would i do to get sin and cos

The reason i am asking is because my nephew has asked me this question before, but because i haven't had a trig problem like this in like 5 or 6 years, i am having trouble remembering how to do this.

He gave me a few problems, and has asked me to find the other 5 functions.

Here is just one.

cot(x) = -12/5
Now i have to find the values of the other 5 functions.

Answer
Hi Sherman,

On a calculator, cos^-1 usually represents arccos.  So, if you have something like

cos(x) = 1/2
then
cos^-1(1/2) = x

In other words, the argument is the value, and the result is the angle.

To get sec, csc and cot, you would need to do the following:

(cos(x))^-1 = sec(x)
or
1/(cos(x)) = sec(x)

The cos^-1 key can be confusing.  Hopefully, this will help you see the difference.  Here is how you can solve your problem.

cot(x) = -12/5
since cot(x) = 1/(tan(x), we can write

tan(x) = -5/12
now we can use arctan(i.e. tan^-1) to find the angle x
x = tan^-1(-5/12)
x = -22.62 degrees

Let me know if you have any questions.

Bobby