MS. MAHER'S MATH



Homework 7.1: Equations of a CircleWrite an equation of a circle with the given center point and radius:(2, 3), r = 5(-3, 0), r=2.5State the center point and radius for the circle which has equation:(x-1)2+x2=36x+22+x-62=256x2+(x+7)2=20(x-3)2+(x+12)2=169Write the equation of a circle with center (-1, 4) and containing the point (5, -4). Use completing the square method to write each equation in standard form, then state the center point and radius, and graph the circle in a coordinate plane.x2+y2+12x=45 x2+y2+14y=-13 x2+y2-2x+6y=3 x+y2-10x+8y=56Homework 7.2: Angles and Coterminal AnglesDirections: 1. Draw the angle with the given measure in standard position. 2. Find one positive and one negative angle coterminal with the given angle. 3. Convert each of your angle measures from degrees to radians.7.3 Right Triangle TrigonometryFind all missing trig functions with the given information.46583602983684sinθ=23;cosθ=55sinθ=67tanθ=3cscθ=1312Lucy is flying a kite with an angle of elevation of 72°. ?The string of the kite is 65 meters long. ?How far is the kite above the ground?Charlie Brown is observing the Washington Monument from 1320 feet away. ?The monument is 555 feet tall. ?What is the angle of elevation to the top of the building?Snoopy is trapped on a tree branch 6.5 meters above the ground. ?Your ladder is only 6.7 meters long. ?If you place the ladder’s tip on the branch, what angle will the ladder make with the ground?Patty is standing a distance away from a skyscraper that is 780 feet tall. ?Patty is between Marcie and the skyscraper. ?The angle of elevation from Marcie’s position to the top of the skyscraper is 42°. ?The angle of elevation from Patty’s position to the top of the skyscraper is 71°. ?How far is Marcie from Patty?Woodstock is in a helicopter is taking pictures of a waterfall that is 240 meters tall. ?The helicopter is hovering 50 meters away from the waterfall and level with its highest point. ?Woodstock is focusing his camera on a point halfway down the waterfall. ?At what angle is the camera lens tilted down from the horizontal?A forester is estimating the amount of lumber contained in a tree. ?When he stands 29 feet away from the tree, the angle to the top of the tree is 55° as measured from his eye-level height, 5 feet above the ground. ?What is the height of the tree?Schroeder is standing 30 feet away from a building. ?His angle of elevation to the top of a window in the building is 65° and to the bottom of the window is 60°. ?What is the height of the window?At a certain distance, the angle of elevation to the top of a building is 60?. From 40 feet further back, the angle of elevation is 45? . Find the height of the building.7.4 Unit CircleDetermine the exact value of each:sin45°cos0sin-210°cos3π4sin4π3cos240°sin8π3cos-90°sin-855°cos570°sin270°cos-π3sin-3π cos11π67.5 Using the Unit CircleDetermine the exact value of each:sin225°cos150°tan60°sinπ6sec2π3cot5π3tan90°cosπcsc3π4sin2πcos-30°sec585°cot180°sinπ2cos270°sec7π6Homework 7.4: Periodic DataDetermine the number of cycles each sine function has in the interval from 0 to 2. Find the amplitude and period of each function.46815597683500253746084455001752608255005. 6. 7.Homework 7.7: The Sine & Cosine GraphWrite an equation for each graph in the form y=asinbθ by finding the number of cycles (b).8. amplitude = 2 period = 9. amplitude = 2.5 period = 2Find the amplitude and period of each sine curve. Then write an equation for each sine function.3082290100965002965451009650012. 13.Determine the number of cycles each sine function has in the interval from 0 to 2π. Find the amplitude and period of each function.14. y = sin 215. y = 3 sin 216. y = 4 sin 5Homework 7.8: Translating the Sine & Cosine Function1. Reasoning The graph at the right shows the sine functions f(), g(), and h(). For each function, a > 0.43159922684700a. Order the functions by increasing value of a.b. Order the functions by increasing value of b.Sketch one cycle of the graph of each sine function. Include the table with the five key points. Show all work for credit.2. y = 2 sin3. y = 3 sin 938862001117600021590635004.5. y = 5 cos 114300123825003657600952500 Write a cosine function for each description. Assume that a < 0. Then, graph the function.6. Amplitude of ? where a<1 and period of for Sine7. Amplitude 2, period 1 for Cosine251341724970038862005524500 ................
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