Jeopardy Exact Values Applications Sinusoids Inverses Fun with

Jeopardy Exact Values Applications Sinusoids Inverses Fun with Unit 2 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500

Exact Values 100 Find the exact value of…. cos 60º Answer: 1/2 BACK

Exact Values 200 Find the exact value of… tan 270º Answer: Undefined BACK

Exact Values 300 Find the exact value of… sec 135º Answer: -√ 2 BACK

Exact Values 400 Find the exact value of… csc 240º Answer: -(2√ 3)/3 BACK

Exact Values 500 Explain why cot 180º is undefined. At 180º, sine is 0 and cosine is -1. So, tangent is 0. But cotangent is the reciprocal of tangent, and the reciprocal of zero is undefined. BACK

Applications 100 Calculate the measure of angle A. 17 m 22 m A Answer: 50. 5994º BACK

Applications 200 How tall is a person whose shadow is 12 feet long when the sun is at an angle of elevation with the ground of 23º. Answer: 5. 0937 ft. BACK

Applications 300 Your cat is stuck 25 feet up a tree. Feeling sorry for the poor creature, you grab a ladder and prop it against the tree to save your cat. If the ladder meets the ground at a 38 degree angle, how long is the ladder? Draw a picture. Answer: 40. 6067 ft. BACK

Applications 400 A ramp is 5 feet long and has a vertical rise of 3. 8 feet. At what angle does it meet the ground? Answer: 49. 46419789º BACK

Applications 500 Imagine you are on a salvage ship in the Gulf of Mexico. Your sonar system has located a sunken Spanish galleon at a slant distance of 683 m from your ship, with an angle of depression of 28º. How deep is the water at the location of the galleon and how far must your ship go to be directly above the galleon? Answer: 321 m and 603 m BACK

Sinusoids 100 Sketch an accurate graph of y = cosθ for 0º < θ < 720º. BACK

Sinusoids 200 Write an equation of the transformed function g(θ) given the parent graph of y = cosθ (in red). Answer: y = cos(θ - 60) + 2 BACK

Sinusoids 300 Write an equation of the transformed function g(θ) given the parent graph of y = sinθ (in red). Answer: y = 3 sin(θ) + 3 BACK

Sinusoids 400 Sketch a graph of y = 1/2 cos(θ) - 1 BACK

Sinusoids 500 Sketch a graph of y = 4 sin(θ – 45º) BACK

Inverses 100 Find the decimal approximation for θ = cos-1(0. 6). What does the answer mean? Answer: θ = 53. 1231º. This is the angle that has a cosine value of 0. 6. BACK

Inverses 200 Find the measure of an angle θ if Tanθ = 5/7. Answer: 35. 5377 degrees BACK

Inverses 300 State the domains of the principal branches sin x, cos x and tan x in order to graph sin-1 x, cos-1 x, and tan-1 x Answer: sin θ -90º < θ < 90º cos θ 0º < θ < 180º tan θ -90º < θ < 90º BACK

Inverses 400 Find the measure of angle C. B 37. 2 cm A 12. 5 cm C Answer: 70. 3654 degrees BACK

Inverses 500 Explain why cos-13 is undefined. Answer: cos-13 represents an angle whose cosine is 3. But the cosine outputs are between -1 < x < 1, and 3 is outside of this range. There is no such angle that will have a cosine of 3. BACK

Fun with Unit 2 100 Fill in the blanks: If f(x) is even, then _______ If f(x) is odd, then _______ Answer: If f(x) is even, then f(-x) = f(x) If f(x) is odd, then f(-x) = -f(x) BACK

Fun with Unit 2 200 Find sinθ and cosθ given that the terminal side of θ contains the point (-5, 7). Answer: sinθ = (7√ 74)/74 cosθ = (-5√ 74)/74 BACK

Fun with Unit 2 300 Given f(x) = 3 x + 1 and g(x) = 2 x 2 + 1, find f(g(x)). Answer: f(g(x)) = 6 x 2 + 4 BACK

Fun with Unit 2 400 For θ = 3411º, sketch the angle in standard position, mark the reference angle, and find the measure of the reference angle. Answer: reference angle is 9º 171º is coterminal to 3411º BACK

Fun with Unit 2 500 Sketch a graph of y = sin(2θ). Highlight one cycle of the graph. What is the period of the graph? Answer: Period is 180º BACK