Misunderstanding the Range: Many students think that the range of inverse trigonometric functions is the same as the regular trigonometric ones. For example, when we look at the function ( y = \sin^{-1}(x) ), its range is actually from (-\frac{\pi}{2}) to (\frac{\pi}{2}), not from (0) to (1).
Confusing the Domain: The domain, or input values, for (\sin^{-1}(x)) is between ([-1, 1]). However, lots of students often use values that are outside this range by mistake.
What are Principal Values?: Inverse functions only give us principal values. Take the function ( y = \tan^{-1}(x) ) for example; it only gives angles between (-\frac{\pi}{2}) and (\frac{\pi}{2}).
Understanding these common mistakes can help students solve problems correctly when dealing with inverse trigonometric functions.
Misunderstanding the Range: Many students think that the range of inverse trigonometric functions is the same as the regular trigonometric ones. For example, when we look at the function ( y = \sin^{-1}(x) ), its range is actually from (-\frac{\pi}{2}) to (\frac{\pi}{2}), not from (0) to (1).
Confusing the Domain: The domain, or input values, for (\sin^{-1}(x)) is between ([-1, 1]). However, lots of students often use values that are outside this range by mistake.
What are Principal Values?: Inverse functions only give us principal values. Take the function ( y = \tan^{-1}(x) ) for example; it only gives angles between (-\frac{\pi}{2}) and (\frac{\pi}{2}).
Understanding these common mistakes can help students solve problems correctly when dealing with inverse trigonometric functions.