121616949-math.105 - 4.10 1 1/2 Inverse Trigonometric...

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4.10 Inverse Trigonometric Functions 91 - 1 1 π/ 2 π ................................ .. . . . . . . . . . ................................. π/ 2 π - 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 4.6 The truncated cosine, the inverse cosine. - π/ 2 π/ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - π/ 2 π/ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - π/ 2 π/ 2 ......................................................... . . . . . . . . . . . . . . . . ........................................................ Figure 4.7 The tangent, the truncated tangent, the inverse tangent. Finally we look at the tangent; the other trigonometric functions also have “partial inverses” but the sine, cosine and tangent are enough for most purposes. The tangent,
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Unformatted text preview: truncated tangent and inverse tangent are shown in figure 4.7 ; the derivative of the arct-angent is left as an exercise. Exercises 1. Show that the derivative of arccos x is-1 √ 1-x 2 . 2. Show that the derivative of arctan x is 1 1 + x 2 . 3. Find the derivative of arccot x , the inverse cotangent. ⇒ 4. Find the derivative of arcsin( x 2 ). ⇒ 5. Find the derivative of arctan( e x ). ⇒ 6. The inverse of cot is usually defined so that the range of arccot is (0 , π ). Sketch the graph of y = arccot x . In the process you will make it clear what the domain of arccot is....
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