Trigonometry

Learning Target O1: I can state the Law of Sines. I can use the Law of Sines to solve triangles. For each of the following, solve the triangle, finding all the missing sides and angles. If more than one triangle is possible, solve BOTH triangles. 1. A = 58°, a = 4.5, b = 12.8 2. A = 36°, B = 65°, c = 10

A hydro pole is stabilized at its top by two guy wires of equal length, each of which makes an angle of 60°with the ground. The wires are secured to the ground at points that are 10 m apart and on opposite sides of the pole. What should the length of each wire be and how tall is the hydro pole? Express your answe rsusing EXACT values! (KN5)

4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car Bis traveling at 45 mph. Which car will reach the intersection first? Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2 points) Part II: Use distance = rate · time to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour. (1 point) Part Ill: Use distance = rate time to determine the time necessary for Car B to reach the intersection. (1 point) Part IV: Which car reaches the intersection first, and by how many hours? (2 points)

Q2. Curriculum expectation: make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and use these connections to solve problems Graph either y=Sin x or y=Cos x (your choice) as a parent function. Apply at least 4different transformations to your parent function, somehow including the values of 5/3, 36, and -2 in your transformations. State the equation of your transformed function and clearly state all|transformations in words. Graph your transformed function.

(10pts) Suppose that cos theta 2/5 =<0 dtermine the value of the other five trignometric functions for this angle

5.) The region in the xy-plane is a circle of radius 4. Cross sections are equilateral triangles.

A pole is supported by two guy wires, as shown. One wire is attached to the top of the pole and the other is attached at the midpoint. a) Determine the height of the pole. b) How far from the base of the pole are the wires anchored?

You are the architectural technician for the firm designing a new building. You need to calculate the width for a parking lot that will surround a building based on customer specifications. The building that measures90 m by 60 m is to be built on the lot and a paved parking lot of uniform width will surround the building.The paved lot is to have an area of 9000 m. Answer the questions that follow.a) How wide is the paved area? Round to the nearest tenth of a metre. (AP7)

\text { Write } \tan \theta \text { in terms of } \cos \theta \text { if } \theta \text { is in Quadrant I. }

Q4. Write any rational function equation (linear over linear) of your choosing where there is a vertical asymptote of x=5/3. Use your equation to determine the x-intercept(s), the y-intercept, and the horizontal asymptote. Sketch a graph of your function from part without using graphing technology.State at least 3 additional characteristics of the function.