126RECEX1 - 7 5 . 7. Suppose cos = 2 3 and 3 2 <...

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MAT 126: Calculus B — Recitation Exercise Sheet #1, Fall 2009 1. Find the interval that satisfies the quadratic inequality: 2 x 2 - 7 x + 3 < 0 . 2. Find and graph the solution to the absolute value inequality: | 3 x - 5 | 6 7 . 3. Consider two points A = (1 , 3) and B = (5 , 6) . Find the equation of the line that contains both of these points in (a) slope-intercept form and (b) point-slope form. 4. (a) Find the equation of the circle with center O = (1 , 4) and radius r = 4 in standard form. (b) Sketch the graph of the region y = 16 - x 2 . What is the resulting shape? 5. (a) Find the equation of the line that is parallel to the line x - 2 y - 1 = 0 and contains the point ( - 3 2 , 3 2 ) . (b) Find the equation of the line that is perpendicular to the line 1 2 x - 1 2 y - 1 2 = 0 and contains the point (1 , - 1) . 6. (a) Convert to radians the degree measure: 120 . (b) Convert to degrees the radian measure: 5 π 3 . (c) Sketch the angle θ = π 6 in standard position. (d) Find an angle coterminal to the angle
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Unformatted text preview: 7 5 . 7. Suppose cos = 2 3 and 3 2 &lt; &lt; 2 , nd the other ve trigonometric functions of . 8. (a) Find all values of [0 , 2 ) such that sin 2 = cos . (b) On the interval [0 , 2 ] sketch the graph of y = cos 2 x. 9. Let = 0 , 6 , 4 , 3 , 2 ,, 3 2 , 2 . (a) Find the exact values for all six trigonometric functions of . (b) For any , state all pythagorean identities, double and half-angle identities, and sum formulas. 10. (a) Compute tan-1 (1) , sin-1 ( 1 2 ) , cos-1 ( 3 2 ) , cos-1 (0) . (b) Prove for any the identity: cos 3 = 4 cos 3 -3 cos . 11. Rewrite as a function of x the expression: log 3 y = 2 + 4 log 3 (2 x ) 12. Let f ( x ) = x 2 for 0 6 x 6 1 . Find L n ,R n ,M n and show that lim n- R n = 1 3 ....
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