The-Organic-Chemistry-Tutor
This video covers the topic of evaluating inverse hyperbolic functions and provides formulas and examples on how to do so. The speaker emphasizes the importance of switching X and Y when dealing with inverse functions and gives formulas for various inverse hyperbolic functions such as cosine, sine, tangent, cotangent, secant, and cosecant. Additionally, the domains for each of these functions are discussed, including potential undefined fractions or values. Finally, the speaker confirms the answers using the exponential function of hyperbolic sine.
In this section, the speaker discusses how to evaluate inverse hyperbolic functions and gives examples. The speaker explains how to switch X and Y when dealing with inverse functions and how to find the inverse hyperbolic cosine function using the formula natural log of x plus the square root of x squared minus one. They also show how to evaluate the inverse hyperbolic sine of one using the formula natural log of x plus the square root of x squared plus one. Finally, the speaker confirms the answers using the exponential function of hyperbolic sine.
In this section, the speaker discusses more formulas related to inverse hyperbolic functions and their corresponding domains. After reviewing the formula for the inverse hyperbolic tangent function, the speaker moves on to discuss the inverse hyperbolic cotangent function, whose formula is very similar. Next, they discuss the inverse hyperbolic secant function and its domain of 0 to 1, with the fraction becoming undefined if we put in zero. Finally, the inverse hyperbolic cosecant function is discussed and its domain is revealed to be all real numbers except zero.
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