Difference between revisions of "The inverse sine, cosine and tangent functions"

Revision as of 16:48, 17 September 2021

$\sin {\theta }=r\to \arcsin {r}=\sin ^{-1}{r}=\theta$

$\cos {\theta }=r\to \arccos {r}=\cos ^{-1}{r}=\theta$

$\tan {\theta }=r\to \arctan {r}=\tan ^{-1}{r}=\theta$

$\csc {\theta }=r\to \operatorname {arccsc} {r}=\csc ^{-1}{r}=\theta$

$\sec {\theta }=r\to \operatorname {arcsec} {r}=\sec ^{-1}{r}=\theta$

$\cos {\theta }=r\to \arccos {r}=\cos ^{-1}{r}=\theta$

Examples:

$\sin {\frac {\pi }{4}}=\sin {\frac {3\pi }{4}}={\frac {sqrt{2}}{2}}\to \arcsin {\frac {sqrt{2}}{2}}={\frac {\pi }{4}}$ , ${\frac {3\pi }{4}}$

@@ Line 12: / Line 12: @@
 <math> \cos{\theta} = r \to \arccos{r} = \cos^{-1}{r} = \theta</math>
-===Examples===
+Examples:
 <math> \sin{\frac{\pi}{4}} = \sin{\frac{3\pi}{4}} = \frac{sqrt{2}}{2} \to \arcsin{\frac{sqrt{2}}{2}} = \frac{\pi}{4} </math>,  <math> \frac{3\pi}{4} </math>