Chapter 4 Essay

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Chapter4 Study Sheet 4.1 Radian Measure: 1) Determine the exact radian measure for each angle. a) 75 75 ×π180= 1.31 rad b) 170 170 ×π180= 2.97 rad c) 280 280 ×π180= 4.89 rad d) 355 355 ×π180= 6.20 rad 2) Determine the exact degree measure for each angle. a) π7 (π7) × (180π) = 25.7 b) 3π12 (3π12) × (180π) = 45 c) 7π20 (7π20) × (180π) = 63 d) 11π14 (11π14) × (180π)= 141.4 3) The back wheel of a bicycle rotates 15 times in 5 seconds. Determine the angular velocity of the wheel in: a) degrees per second a) 1500×36060 = 9000 /second b) radians per second b) 1500×2π60 = 157 rad /second 4) Find the length of the arc length of a circle with radius 10cm and central angle of 6.5 radian. θ = ar (a = arc length, r= radius) 6.5 =a10 so, a = 65cm 4.2 Special Angles and Unit Circle: 1). Determine an exact value for each expression. a) sin11π6cos7π6 + sin5π3cos4π3=-12×-32+-32×-12=32 b) sin3π4cos3π4 - sinπ6cos5π4=22×-22-12×-22=2-24 2). Philip is flying his paper plane at the end of a 90m string. The sun is directly overhead, and the string makes an angle of 11π6with the ground. The wind speed increases, and the kite flies higher until the string makes an angle of 5π3with the ground. a) Determine an exact expression for the horizontal distance that the shadow of the paper plane moves between the two positions of the paper plane. cos11π6=x190 32=x190 so, x1=453 cos5π3=x290 1 2= x290 so, x2=45 Y = 453 -45=45(3-1)m b) Determine the distance in part a), to the nearest hundred of a metre. 45(3-1) = 32.94m 4.4 Compound Angles Formulas: 1). Using a compound angle formula determine the exact values for each of the following. a). cos9π4 cos9π4×180π=405°= 360°+45°=cos(2π+π4)=22 b). sin11π12 sin11π12×180π=165°=135°+30°=sin(3π4+π6)=6-24 c).

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