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Unformatted text preview: Chapter 10 Trigonometric functions 10.1 Calculate the first derivative for the following functions. (a) y = sin x 2 (b) y = sin 2 x (c) y = cot 2 3 x (d) y = sec( x 3 x 2 ) (e) y = 2 x 3 tan x (f) y = x cos x (g) y = x cos x (h) y = e sin 2 1 x (i) y = (2 tan3 x + 3 cos x ) 2 (j) y = cos(sin x ) + cos x sin x 10.2 Take the derivative of the following functions. (a) f ( x ) = cos(ln( x 4 + 5 x 2 + 3)) (b) f ( x ) = sin( radicalbig cos 2 ( x ) + x 3 ) (c) f ( x ) = 2 x 3 + log 3 ( x ) (d) f ( x ) = ( x 2 e x + tan(3 x )) 4 (e) f ( x ) = x 2 radicalbig sin 3 ( x ) + cos 3 ( x ) v.2005.1  September 4, 2009 1 Math 102 Problems Chapter 10 10.3 Convert the following expressions in radians to degrees: (a) (b) 5 / 3 (c) 21 / 23 (d) 24 Convert the following expressions in degrees to radians: (e) 100 o (f) 8 o (g) 450 o (h) 90 o Using a Pythagorean triangle, evaluate each of the following: (i) cos( / 3) (j) sin( / 4) (k) tan( / 6) 10.4 Graph the following functions over the indicated ranges: (a) y = x sin( x ) for 2 < x < 2 (b) y = e x cos( x ) for 0 < x < 4 . 10.5 Sketch the graph for each of the following functions: (a) y = 1 2 sin 3( x 4 ) (b) y = 2 sin x (c) y = 3 cos 2 x (d) y = 2 cos( 1 2 x + 4 ) 10.6 The Radian is an important unit associated with angles. One revolution about a circle is equivalent to 360 degrees or 2 radians. Convert the following angles (in degrees) to angles in radians. (Express these as multiples of , not as decimal expansions): (a) 45 degrees (b) 30 degrees (c) 60 degrees (d) 270 degrees. Find the sine and the cosine of each of these angles. v.2005.1  September 4, 2009 2 Math 102 Problems Chapter 10 10.7 A point is moving on the perimeter of a circle of radius 1 at the rate of 0.1 radians per second. How fast is its x coordinate changing when x = 0 . 5? How fast is its y coordinate changing at that time? 10.8 The derivatives of the two important trig functions are [sin( x )] prime = cos( x ) and [cos( x )] prime = sin( x )....
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 Winter '10
 Lioudmila

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