126RECEX1 - 7 π 5 7 Suppose cos θ = 2 3 and 3 π 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 π 5 . 7. Suppose cos θ = 2 3 and 3 π 2 < θ < 2 π, find the other five trigonometric functions of θ. 8. (a) Find all values of θ ∈ [0 , 2 π ) such that sin 2 θ = cos θ. (b) On the interval [0 , 2 π ] sketch the graph of y = cos 2 x. 9. Let θ = 0 , π 6 , π 4 , π 3 , π 2 ,π, 3 π 2 , 2 π. (a) Find the exact values for all six trigonometric functions of θ. (b) For any θ, 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 θ the identity: cos 3 θ = 4 cos 3 θ-3 cos θ. 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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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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