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Unit Circle – Class WorkFind the exact value of the given expression.cos4π32. sin7π43. sec2π3tan-5π65. cot15π46. csc-9π2Given the terminal point 37,-2107 find tanθGiven the terminal point -513,-1213 find cotθKnowing cosx=23 and the terminal point is in the fourth quadrant find sinx.Knowing cotx=45 and the terminal point is in the third quadrant find secx.Unit Circle – Home WorkFind the exact value of the given expression.cos5π312. sin3π413. sec4π3tan-7π615. cot13π416. csc-11π2Given the terminal point 725,-2425 find cotθGiven the terminal point -429,79 find tanθKnowing sinx=78 and the terminal point is in the second quadrant find secx.Knowing cscx=-45 and the terminal point is in the third quadrant find cotx.Graphing – Class WorkState the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.y=2cos2x+π3+122. y=-3cos4x-π-2y=sin23x+π6+324. y=-1cos3x-2π-1y=23cos4x-2π+2Graphing – Home WorkState the amplitude, period, phase shift, and vertical shift for each function. Draw the graph by hand and then check it with a graphing calculator.y=-4cos12x-π3+227. y=-2cos4x-3π-3y=2sin14x+π2+129. y=-1cos6x-2π-1y=32cos4x-3π-2Law of Sines – Class WorkSolve triangle ABC.A=70°,B=30°,c=432. B=65°,C=50°,a=12b=6, A=25°,B=45°34. c=8, B=60°,C=40°c=12,b=6,C=70°36. b=12,a=15, B=40°A=35°,a=6, b=11An airplane is on the radar at both Newark Liberty International and JFK airports that are 20 miles apart. The angle of elevation from Newark to the plane is 42°and from JFK is 35° when the plane is directly between them. How far is the plane from JFK? What is the plane’s elevation?A mathematician walking in the woods noticed that the angle the angle of elevation to a bird at the top of a tree is 50°, after walking 40’ toward the tree, the angle is 55°. How far is she from the bird?Law of Sines – Home WorkSolve triangle ABC.A=60°,B=40°,c=541. B=75°,C=50°,a=14b=6, A=35°,B=45°43. c=8, B=50°,C=40°c=12,b=8,C=65°45. b=12,a=16, B=50°A=40°,a=5, b=12An airplane is on the radar at both Newark Liberty International and JFK airports that are 20 miles apart. The angle of elevation from Newark to the plane is 52°and from JFK is 45° when the plane is directly between them. How far is the plane from JFK? What is the plane’s elevation?A mathematician walking in the woods noticed that the angle the angle of elevation to a bird at the top of a tree is 45°, after walking 30’ toward the tree, the angle is 60°. How far is she from the bird?Law of Cosines – Class WorkSolve triangle ABC.a=3,b=4,c=650. a=5,b=6,c=7a=7,b=6,c=452. A=100°,b=4,c=5B=60°,a=5,c=954. C=40°,a=10, b=12A ship at sea noticed two lighthouses that according to the charts are 1 mile apart. The light at lighthouse A is 200’ above sea level and the navigator on the ship measures the angle of elevation to be 2°, how far is the ship from lighthouse A? The light at lighthouse B is 300’ above sea level and the navigator on the ship measures the angle of elevation to be 5°, how far is the ship from lighthouse B? How far is the ship from shore?A student takes his 2 dogs for a walk. He lets them off their leash in a field where Edison runs at 7 m/s and Einstein runs at 6 m/s. The student determines the angle between the dogs is 20°, how far are the dogs from each other in 8 seconds?Law of Cosines – Home WorkSolve triangle ABC.a=4,b=5,c=858. a=4,b=10,c=13a=11,b=8,c=660. A=85°,b=3,c=7B=70°,a=6,c=1262. C=25°,a=14, b=19A ship at sea noticed two lighthouses that according to the charts are 1 mile apart. The light at lighthouse A is 275’ above sea level and the navigator on the ship measures the angle of elevation to be 4°, how far is the ship from lighthouse A? The light at lighthouse B is 325’ above sea level and the navigator on the ship measures the angle of elevation to be 8°, how far is the ship from lighthouse B? How far is the ship from shore?A student takes his 2 dogs for a walk. He lets them off their leash in a field where Edison runs at 10 m/s and Einstein runs at 8 m/s. The student determines the angle between the dogs is 25°, how far are the dogs from each other in 5 seconds?Pythagorean Identities – Class WorkSimplify the expressioncscxtanx66. cotxsecxsinxsinxcscx-sinx68. 1+cot2x1-cos2x1-tan2xsec2x 70. sinx-cosx2cot2x1-sin2x72. cosxsecx+tanxsinxtanx+cosxVerify the Identity1-sinx1+sinx=cos2x75. tanxcotx secx=cosx1-cos2x1+tan2x=tan2x77. 1secx+tanx+1secx-tanx=2secxPythagorean Identities – Home WorkSimplify the expressiontanx+cotx 279. 1-sinxcosx+cosx1-sinxcosx-cosysinx+siny+sinx-sinycosx+cosy81. 1sinx-1cscx1+sec2x1+tan2x83. sin2xtan2x+cos2xcot2xtan2x1+tan2x85. cosxsecx+sinxcscx1+sec2x1+tan2x+cos2xcot2xVerify the Identitycos2x-sin2x=1-2sin2x88. tanxcosxcscx=1 1+cotxcscx=sinx+cosx90. cosxcscxcotx=1Angle Sum/Difference Identity – Class WorkUse Angle Sum/Difference Identity to find the exact value of the expression.sin10592. cos75tan19594. sin-π12cos19π1296. tan-π12Verify the Identity.sinx+π3+sinx-π3=sinx98. cosx+π4cosx-π4=cos2x-12tanx-π4=tanx-1tanx+1100. sinx+y-sinx-ycosx+y+cosx-y=tanyAngle Sum/Difference Identity – Home WorkUse Angle Sum/Difference Identity to find the exact value of the expression.sin165102. cos105tan285104. sin-11π12cos17π12106. tan-7π12Verify the Identity.sinx+2π3+sinx-2π3=-sinx108. cosx+3π4cosx-3π4=cos2x-12tanx+5π4=tanx+11-tanx110. cos5π6+xcos5π6-x=34-sin2xDouble Angle Identity – Class WorkFind the exact value of the expression. cosθ=14,findcos2θ if θ is in the first quadrant.cosθ=14,findsin2θ if θ is in the fourth quadrant.sinθ=-37,findtan2θ if θ is in the third quadrant.sinθ=-37,findcos2θ if θ is in the fourth quadrant.tanθ=-59,findsin2θ if θ is in the second quadrant.cotθ=59,findtan2θ if θ is in the third quadrant.Verify the Identity.sin3x=3sinx-4sin3x118. tan3x=3tanx-tan3x 1-3tan2xsin4xsinx=4cos2x cos x120. csc2x=cscx 2cosxDouble Angle Identity – Home WorkFind the exact value of the expression. cosθ=34,findcos2θ if θ is in the first quadrant.cosθ=34,findsin2θ if θ is in the fourth quadrant.sinθ=-57,findtan2θ if θ is in the third quadrant.sinθ=-57,findcos2θ if θ is in the fourth quadrant.tanθ=-49,findsin2θ if θ is in the second quadrant.cotθ=49,findtan2θ if θ is in the third quadrant.Verify the Identity.sec2x=sec2x2-sec2x128. 1+sin2xsin2x=1+12secxcscx1+cos10x=2cos25xHalf Angle Identity – Class WorkFind the exact value of the expression.1-cos6x2131. cos2x2-sin2x2sin22.5133. tan67.5Verify the Identity.secx2=±2tanxtanx+sinxHalf Angle Identity – Home WorkFind the exact value of the expression.1+cos4x2136. 2cosx2sinx2cos22.5138. tan15Verify the Identity.tanx2=cscx-cotxPower Reducing Identity – Class WorkSimplify the expression.cos4x141. sin8xsin4x cos2xFind sinθ2 if cosθ=35 and θ is in the first quadrant.Find cosθ2 if tanθ=35 and θ is in the third quadrant.Power Reducing Identity – Home WorkSimplify the expression.sin2x cos2x146. sin4x cos4xsin2x cos4xFind sinθ2 if cosθ=35 and θ is in the fourth quadrant.Find cosθ2 if sinθ=-47 and θ is in the third quadrant.Sum to Product Identity – Class WorkFind the exact value of the expression.sin75+sin15151. cos75 –cos15152. cos75+cos15Verify the Identity.sinx+ sin5xcosx+cos5x=tan3x154. sinx + sinycosx-cosy=-cotx-y2155. cosx+cos3xsin3x-sinx=cotxSum to Product Identity – Home WorkFind the exact value of the expression. sin105+sin15157. cos105 –cos15158. cos105+cos15Verify the Identity.cos4x+cos2xsin4x+sin2x=cot3x160. sinx+sin5x+sin3xcosx+cos5x+cos3x=tan3xcos87+cos33=sin63Product to Sum Identity – Class WorkFind the exact value of the expression.cos75cos15163. sin37.5sin7.52sin52.5cos97.5165. 10cos6xsin4xProduct to Sum Identity – Home WorkFind the exact value of the expression.cos37.5cos7.5167. sin45sin154cos195sin15169. 3sin8xcos2xInverse Trig Functions – Class WorkEvaluate the expression.sincos-1513170. costan-1-65tansin-134172. sintan-1-713cossin-1611174. tancos-1-35sin-1sinπ4176. sin-1sin3π4cos-1cosπ3178. cos-1cos-π3Inverse Trig Functions – Home WorkEvaluate the expression.sincos-11213180. costan-1-75tansin-114182. sintan-1-513cossin-1911184. tancos-1-45sin-1sinπ6186. sin-1sin5π6cos-1cos2π3188. cos-1cos-2π3Trig Equations – Class WorkFind the value(s) of x such that 0≤x<2π, if they exist.sinx=1190. 3tan2x=1sec2x-2=0192. 2sin2x+3=7sinxcsc2x=4194. 3sec2x=4sin2x-cosxsinx=0196. 2sinx+1=cos2xsin2x +cosx=0198. sinx2+cosx=0cos2x+cosx=2Trig Equations – Home WorkFind the value(s) of x such that 0≤x<2π, if they exist.cosx=-1201. 2sin2x=1csc2x-2=0203. 2sin2x-3=sinxsec2x=4205. 3csc2x=4cos2x-cosxsinx=0207. sinx-1=-2cos2xsin2x =2tan2x209. tanx2-sinx=0sin2x-sinx=0Trigonometry Unit ReviewMultiple ChoiceGiven the terminal point of 22,-22 find tanθ.π4-π4-11Knowing secx=-54 and the terminal point is in the second quadrant find cotθ.-4535-43-34What is the phase shift of y=53cos6x-2π+3?12ππ3132πThe difference between the maximum of y=2cos2x+π3+1 and y=-3cos4x-π-2 is1238Given ?ABC, with A=35°,a=5, & c=7, find B.18.41853.41891.582both a and bGiven ?ABC, with A=50°,a=6, & c=8, find B.1.02140128.979no solutionGiven ?ABC, with A=50°,b=6, & c=8, find B.6.18832.45647.96782.033secx+tanxsecx-tanx=1+2secxtanx1-secxtanx 1-2sinxcos2x1Find the exact value of sinπ126-246+246-226-22On the interval 0,2π, sin2x=0, thus x =0π23π2all of the aboveFind the exact value of cos1052-32-2-322+32-2+32sin4x=183-cosx+cos4x183+cosx+cos4x183+4cosx+cos4x183-4cosx+cos4xRewrite cos6xsin4x as a sum or difference.12cos10x-12cos2x12cos10x+12cos2x12sin10x-sin2x12sin10x-12sin2xOn the interval 0,2π, sin5x+sin3x=0π4kπ4, where k∈Integerskπ4, where k∈0,1,2,6no solution on the interval givensin-1sin4π3=4π3-π3both a and bUndefinedOn the interval 0,2π, solve 2sin2x+3cosx=3I. 0 II. π3 III. 5π3I onlyII and IIII and IIII, II, and IIIExtended ResponseThe range of a projectile launched at initial velocity v0 and angle θ, isr=116v02sinθcosθ,where r is the horizontal distance, in feet, the projectile will travel.Rewrite the formula using double angle formula.A golf ball is hit 200 yards, if the initial velocity 200 ft/sec, what was the angle it was hit?If the golfer struck the ball at 45°, how far would the ball traveled?A state park hires a surveyor to map out the park.A and B are on opposite sides of the lake, if the surveyor stands at point C and measures angle ACB= 50 and CA= 400’ and CB= 350’, how wide is the lake?At a river the surveyor picks two spots, X and Y, on the same bank of the river and a tree, C, on opposite bank. Angle X= 60 and angle Y= 50 and XY=300’, how wide is the river? (Remember distance is measured along perpendiculars.)The surveyor measured the angle to the top of a hill at the center of the park to be 32°. She moved 200’ closer and the angle to the top of the hill was 43°. How tall was the hill?The average daily production, M (in hundreds of gallons), on a dairy farm is modeled byM=19.6sin2πd365+12.6+45where d is the day, d=1 is January first.What is the period of the function?What is the average daily production for the year?Using the graph of M(d), what months during the year is production over 5500 gallons a day?A student was asked to solve the following equation over the interval 0,2π. During his calculations he might have made an error. Identify the error and correct his work so that he gets the right answer. cosx+1=sinxcos2x+2cosx +1=sin2xcos2x+2cosx +1=1-cos2x2cosx=0cosx=0π2,3π2 ................
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