The derivatives of inverse trig functions can be written in alternative notation as follows:d/dx (sin-1x) = 1/√1-x² d/dx(cos-1x) = -1/√1-x² d/dx(tan-1x) = 1/(1+x²) d/dx(csc-1x) = -1/(|x|√x²-1) d/dx(sec-1x) = 1/(|x|√x²-1) d/dx(cot...
What is the inverse of the function f(x) = (1/9)x + 2? What is the inverse function of f(x) = 3x - 3? What is the inverse of the function f(x) = 64x^2 when x is greater than or equal to 0? What is the inverse of f(x) = 2x + 8?
Here we have the function f(x) = 2x+3, written as a flow diagram:The Inverse Function goes the other way:So the inverse of: 2x+3 is: (y−3)/2The inverse is usually shown by putting a little "-1" after the function name, like this:f-1(y)...
When we need to use them, we can derive these formulas by using the trigonometric relations between the angles and sides of a right triangle, together with the use of Pythagoras’s relation between the lengths of the sides. We can use the Pythagorean identity, sin2x+cos2x=1sin2x+cos...
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The integrals of inverse trig functions are tabulated below:Inverse Trig FunctionIntegral ∫ sin-1x dx x sin-1x + √(1 - x²) + C ∫ cos-1x dx x cos-1x - √(1 - x²) + C ∫ tan-1x dx x tan-1x - (1/2) ln |1 + x²| + C ∫ csc-1x dx x csc-1x + ...
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For example, consider the function f(x)=x3+4f(x)=x3+4. Since any output y=x3+4y=x3+4, we can solve this equation for xx to find that the input is x=3√y−4x=y−43. This equation defines xx as a function of yy. Denoting this function as f−1f−1, and writing x=f...
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Sometimes, you will encounter the composition of trig functions with inverse trig functions. The following are pretty straightforward compositions. Did you suspect the answer was going to be 120o? This problem behaved differently because 120o is outside the range of the arcsin. So use some cautio...