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5 The equation of the line through (1, 2) that is perpendicular to y = 3x + 6 is (a) y 1 = [1/3](x 2) (b) y 2 = 3(x 1) (c) y = [1/3](x + 1) (d) y 2 = [ 1/3](x 1) (e) y 2 = [1/3](x 1) 6 The equation of the line through ( 2, 5) that is parallel to y = 4x + 2 is (a) y 5 = 4(x + 2) (b) y 2 = 4(x + 5) (c) y + 5 = 4(x 2) (d) y 5 = 4(x 2) (e) y + 2 = 4(x 5) 7 The line passing through the points (2, 1) and (5, 3) has equation (a) y + 2 = [3/2](x + 1) (b) y 2 = [2/3](x 1) (c) y 1 = [ 2/3](x 2) (d) y 1 = [2/3](x 2) (e) y + 1 = [2/3](x + 2) 8 The equation y + y2 3x + 2 = 0 describes (a) a circle (b) a parabola (c) a line (d) a cardioid (e) an ellipse 9 The curve y = x 3 intersects the line y = x (a) in a segment (b) in a circle (c) in an arc (d) in two points (e) in one point 10 The sine of an angle is always (a) between 1 and 2 inclusive (b) between 1 and 0 exclusive (c) between 1 and 1 inclusive

10-12

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11 Graph each of these functions on a separate set of axes Label your graph (a) f (x) = x 2 3x x+1 (b) g (x) = 2x (c) h(x) = x 2 x (d) f (x) = 2x + 1 (e) g (x) = x 2 + x (f) h(x) = x + 5 12 Calculate each of the following trigonometric quantities (a) sin(2 /3) (b) tan( /6) (c) sec(3 /4) (d) csc(5 /4) (e) cot( 11 /4) (f) cos( /4) 13 Calculate the left and right sides of the twelve fundamental trigonometric identities for the values = /6 and = /3, thus confirming the identities for these particular values 14 Sketch the graphs of each of the following trigonometric functions (a) f (x) = cos 2x (b) g (x) = sin(x /2) (c) h(x) = cot(x + ) (d) f (x) = tan(x + ) (e) g (x) = cos(x/6) (f) h(x) = cos( + [x/2]) 15 Convert each of the following angles from radian measure to degree measure (a) = /12 (b) = /2 (c) = 27 /4 (d) = 3 /16 (e) = 4 (f) = 7 16 Convert each of the following angles from degree measure to radian measure (a) = 45 (b) = 20

Note that the jerk values equal zero except where that value is in nite at the points of acceleration discontinuity

(c) (d) (e) (f)

This curve (follower motion) of the polynomial family has a triangular acceleration curve It is a modi cation of the parabolic curve, eliminating the abrupt change in acceleration at the beginning and the end of the stroke However it does have an acceleration discontinuity at the midpoint This curve has limited applications since it also has high velocities and high acceleration values, giving excessive pressure angle and inertia forces It is not very practical except when combined with other curves The construction of this curve (Fig 26) is similar to that of the acceleration curve previously with the increments being 1, 7, 19, and so forth, which is a cubic relationship in lieu of 1, 3, 5 as with the constant acceleration curve Thus it will not be shown here By methods shown for the parabolic curve, we can solve the cubic curve for 0 q b 2

Solution: Recognizing that cosx is the derivative of sin x suggests a change of variable might make this integral into a standard form Take U = sin x and du = cosxdx Making these substitutions

Jerk y''' =

= 55 = 100 = 2 = 314

y, y', y", y'''

.

Acceleration, y"

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