Difference between revisions of "The inverse sine, cosine and tangent functions"
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===Notation of Inverse Trig Functions=== | ===Notation of Inverse Trig Functions=== | ||
− | <math> \sin{\theta} = r \to \arcsin{r} = \sin^{-1}{r} = \theta</math>. The domain of <math> y = \arcsin{x} | + | <math> \sin{\theta} = r \to \arcsin{r} = \sin^{-1}{r} = \theta</math>. The domain of <math> y = \arcsin{x} </math> is <math>[-1,1]</math>, and its range is <math>[\frac{-\pi}{2}, \frac{\pi}{2}]</math>. |
<math> \cos{\theta} = r \to \arccos{r} = \cos^{-1}{r} = \theta </math> | <math> \cos{\theta} = r \to \arccos{r} = \cos^{-1}{r} = \theta </math> | ||
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Examples: | Examples: | ||
− | + | * <math> \sin{\frac{\pi}{4}} = \frac{\sqrt{2}}{2} \to \arcsin{\frac{\sqrt{2}}{2}} = \frac{\pi}{4} </math>. Even though <math> \sin{\frac{3\pi}{4}} = \frac{\sqrt{2}}{2}</math> as well, <math> \frac{3\pi}{4} </math> is outside of the range for <math> \arcsin{x} \theta</math>. | |
− | <math> \sin{\frac{\pi}{4}} = \frac{\sqrt{2}}{2} \to \arcsin{\frac{\sqrt{2}}{2}} = \frac{\pi}{4} | ||
==Resources== | ==Resources== | ||
* [https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions-intro Intro to Inverse Trig Functions], Khan Academy | * [https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions-intro Intro to Inverse Trig Functions], Khan Academy | ||
* [https://tutorial.math.lamar.edu/extras/algebratrigreview/inversetrig.aspx Inverse Trig Functions], Paul's Online Notes | * [https://tutorial.math.lamar.edu/extras/algebratrigreview/inversetrig.aspx Inverse Trig Functions], Paul's Online Notes |
Revision as of 16:55, 17 September 2021
Notation of Inverse Trig Functions
. The domain of is , and its range is .
Examples:
- . Even though as well, is outside of the range for .
Resources
- Intro to Inverse Trig Functions, Khan Academy
- Inverse Trig Functions, Paul's Online Notes