# Thread: The 6 Trigonometric values

1. ## The 6 Trigonometric values

Find the 6 trigonometric values of theta= cos^-1 (3/7)

Now I was thinking cos^-1 = (3/7) is equivalent to secant=3/7 right? Meaning cosine would be 7/3. I draw my triangle, and solve for the last side by using pythagorean theorem. When I have all three sides I can identify my remaining 4 trigonometric values. Is this right?

2. Originally Posted by fezz349
Find the 6 trigonometric values of theta= cos^-1 (3/7)

Now I was thinking cos^-1 = (3/7) is equivalent to secant=3/7 right? Meaning cosine would be 7/3. I draw my triangle, and solve for the last side by using pythagorean theorem. When I have all three sides I can identify my remaining 4 trigonometric values. Is this right?
$\displaystyle \theta = \cos^{-1}(x)$ is not a reciprocal function, it's the inverse cosine function.

if $\displaystyle \theta = \cos^{-1}\left(\frac{3}{7}\right)$ , then $\displaystyle \cos{\theta} = \frac{3}{7}$

note that $\displaystyle \theta$ in this case is restricted to quad I because the range of the inverse cosine function is $\displaystyle [0,\pi]$

3. is not a reciprocal function, it's the inverse cosine function.

if , then

note that in this case is restricted to quad I because the range of the inverse cosine function is

hmm... i don't remember learning that in class to be honest. i hope you don't mind me asking a couple questions to clear things up so I can better understand and work through this. What's the difference between a reciprocal function and an inverse function, and what about this inverse cosine function makes it so costheta=3/7 is equivalent to cos^-1(3/7). If you're speaking about an inverse in any situation doesn't that generay mean to opposite?

4. thanks a lot skeeter ^_^