Limit Evaluation Methods Continuous Functionsĭerivatives Math Help Definition of a Derivative
The following expression states that as x approaches infinity, the value c is a very large and positive number, the function approaches the value L.Īlso the limit as x approaches negative infinity, the value of c is a very large and negative number, is expressed below. The following expression states that as x approaches the value c and x < c the function approaches the value L. The following expression states that as x approaches the value c and x > c the function approaches the value L. The following expression states that as x approaches the value c the function approaches the value L. This value can be any point on the number line and often limits are evaluated as an argument approaches infinity or minus infinity.
( )sin ωθ → 2T π ω = ( )cos ωθ → 2T π ω = ( )tan ωθ → T π ω = ( )csc ωθ → 2T π ω = ( )sec ωθ → 2T π ω = ( )cot ωθ → T π ω = θ adjacent opposite hypotenuse x y ( ),x y θ x y 1 © 2005 Paul Dawkins Formulas and Identities Tangent and Cotangent Identities sin costan cot cos sin θ θ θ θ θ θ = Reciprocal Identities 1 1csc sin sin csc 1 1sec cos cos sec 1 1cot tan tan cot θ θ θ θ θ θ θ θ θ θ θ θ = Pythagorean Identities 2 2 2 2 2 2 sin cos 1 tan 1 sec 1 cot csc θ θ θ θ θ θ + = + = + = Even/Odd Formulas ( ) ( ) ( ) ( ) ( ) ( ) sin sin csc csc cos cos sec sec tan tan cot cot θ θ θ θ θ θ θ θ θ θ θ θ − = − − = − − = − = − = − − = − Periodic Formulas If n is an integer.The limit is a method of evaluating an expression as an argument approaches a value. So, if ω is a fixed number and θ is any angle we have the following periods. 1 sin 1θ− ≤ ≤ csc 1 and csc 1θ θ≥ ≤ − 1 cos 1θ− ≤ ≤ sec 1 andsec 1θ θ≥ ≤ − tanθ−∞ < < ∞ cotθ−∞ < < ∞ Period The period of a function is the number, T, such that ( ) ( )f T fθ θ+ =. sin 1 y yθ = 1csc y θ = cos 1 x xθ = 1sec x θ = tan y x θ = cot x y θ = Facts and Properties Domain The domain is all the values of θ that can be plugged into the function. oppositesin hypotenuse θ = hypotenusecsc opposite θ = adjacentcos hypotenuse θ = hypotenusesec adjacent θ = oppositetan adjacent θ = adjacentcot opposite θ = Unit circle definition For this definition θ is any angle. Download Trigonometry Cheat Sheet for Calculus and more Trigonometry Cheat Sheet in PDF only on Docsity!Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 π θ< < or 0 90θ° < < °.
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