Waukee Community School District Blogs



Section 2.1If A and B are complementary angles then cos A = sin B. Sine and cosine are cofunctions.Cofunction Identitiessin A = cos(90° - A)cos A = sin(90° - A)sec A = csc(90° - A)csc A = sec(90° - A)tan A = cot(90° - A)cot A = tan(90° - A)45° - 45° - 90° Triangles30° - 60° - 90° Triangles1. Find the sine, cosine, and tangent values for angle A and B.2. Given a right triangle ABC, and the given values find all 6 trigonometric values.a) a = 3, c = 102. Given a right triangle ABC, and the given values find all 6 trigonometric values.b) a = 8, b = 113. Writing Functions in terms of its co-functions.a) cos 52b) tan 71c) sec 244. Solving Equations using co-function identities.a) cos( + 4) = sin(3 + 2)b) tan(2 - 18) = cot( + 18)c) sec(3 + 10) = csc( + 8)4. Determine whether the statement is true or false.a) sin 21 > sin 18b) sec 56 < sec 49Find the exact value of each.tan 30°sin 30°sec 30°csc 45°cos 45°sin 60 °tan 60°Section 2.2A _____________________ angle is a positive acute angle measured from the terminal side of an angle to the ___________________Reference AnglesAn angle ’ is a positive acute angle made by the terminal side of the angle and the x-axis.-228600135255A reference angle can be expressed as a 30°, 45°, or a 60° angle and then we can use the information that we know from those triangles to find the values of the six trig functions of the reference angle.1. Find the reference angles for the given angle.a) 278b) -125 c) 99d) -13872. Find the 6 trig functions for each angle. Use reference angles.a) 210b) - 315c) 1203. Evaluating Expressions with Functional Values of Special Anglescos 120 + sin2 60 - tan2 30cos2 60 + sec2 150 - csc2 2104. Find all values of , if is an angle [0,360] for each.1143000157480a) cos = b) tan =undefinedc) csc = 2Section 2.3Calculators can be used to find the values of the six trig functions for angles. The angles must be written as a ________________ to be entered into the calculator. Make sure your calculator is in _______________ modeSin, Cos, and Tan are used to convert _____________ to ratios.02286000are used to convert ______________ to angles1.Calculate the value of each expression.a) sin 49 12’b) sec 97.977c) cos(-246)d) 1/cot(51.4283)e) tan77f) csc(-140)2. Finding Angle Measures using a calculator.a) sin = .9677b) sec = 1.054c) tan = 5.876Section 2.4Trig functions are used to solve ___________ triangles.Angles of ____________________ are measured from a horizontal line up to the line of sight to the object.Angles of _______________________ are measured from a horizontal down to the line of sight to the object.1. 2. 3.4. How tall is a flagpole that casts a 12-foot shadow when the sun is at an angle of 75° above the horizon?A kite on the end of a 250-foot string is at an angle of 35° above horizontal. How high is the kite above the ground? Assume the string is a straight line.For safety and noise abatement, landing aircraft are required to be 1500 feet above the ground when they are 25000 feet from the end of the runway (horizontal distance). What is the angle of the glide slope that makes this possible?An airplanes distance measuring equipment measures the slant range distance from the aircraft to the navigational aid. If an aircraft is 17.56 miles slant range distance from a navigational aid and is flying two miles above the ground, what is the distance along the ground from the airplane to the navigational aid? Do not use the Pythagorean Theorem.Section 2.5The term _______________ is used in navigation to designate a direction. If the bearing is expressed only in degrees, it is measured from a _________________line.Bearings may also be measured from either a _______________ or _____________ line and would be expressed in terms such as N35°W or S50°E. 1. 2. 3. A surveyor on a mountain road 524 feet above a lake was asked to calculate the distance across the lake. The surveyor measured the angle of depression to the near and far edges of the lake to be 66° and 27° respectively. Determine the distance across the lake.To determine the height of a mountain, a surveyor measured the angle of elevation to the top of the mountain from two points 500 feet apart. The two angles of elevation were 35° and 40°. To the nearest 10 feet, how high is the mountain?Veronica and Jose are located one mile apart on the ground. They observe a blimp directly above the road connecting them. Jose measures the angle of elevation to the blimp to be 53°; Veronica measures the angle of elevation to the blimp as 22°. Find the height of the blimp above the ground.The Empire State Building is observed directly south of tourist A. A second tourist is 15 miles due west from tourist A finds the bearing to the Empire State Building to be S35.7°E. How far is the Empire State Building from tourist B? ................
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