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Click here for Final Jeopardy Graphing Inverse Trig Functions Word Problems Trig Identities Solving Equations 10 Point 10 Point 10 Point 10 Point 10 Point 20 Points 20 Points 20 Points 20 Points 20 Points 30 Points 30 Points 30 Points 30 Points 30 Points 40 Points 40 Points 40 Points 40 Points 40 Points 50 Points 50 Points 50 Points 50 Points 50 Points Graph this equation: y = tan (x) Question 1a Graph this equation: y = sec (x) Question 2a Graph this equation: y = sin 2x, if 0≤x≤π Question 3a Graph this equation: y=3+5sin (πx+π/4), from -2 to 2 Question 4a Find the equation of the following graph y= -5 cos (πx-π/2) Find the inverse of the following graph y=(x+3)/2 Find the inverse for the following equation: y=x²-4 y= +/- √(x+4) Find and graph the inverse of this equation: y= sin x y= arcsin (x) Evaluate the following equation: sin(arctan 3/4) 3/5 Write the expression sin (arccos x) as an equivalent expression in x only (assume x is positive) sin (arccos x) = sin θ=√(1-x2)/1 = If a 75.0-ft flagpole casts a shadow 43.0 ft long, what is the angle of the elevation of the sun from the tip of the shadow, to the nearest 10minute interval? 60 degrees, 10' San Luis, California, is 12 mi due north of Grover Beach. If Arroyo Grande is 4.6 mi east of Grover Beach, what is the bearing of San Luis from Arroyo Grande? N 21 degrees W Tom is walking down the hall, when he catches a glimpse of himself in a mirror. Tom notices that the angle of depression from his eyes to the bottom of the mirror is 12 degrees, while the angle of elevation to the top of the mirror is 11 degrees. Tom is standing 150 cm from the mirror. Find the vertical dimension of the mirror. 61 cm From a point on the floor the angle of elevation to the top of a door is 47 degrees, while the angle of elevation to the ceiling above the door is 59 degrees. If the ceiling is 10 feet above the floor, what is the vertical dimension of the door? 6.4 feet A satellite (point A) is circling 112 miles above the earth, as shown below. When the satellite is directly above point B, angle A is found to be 76.6 degrees. Use this information to fine the radius of the earth. 4,000 miles Prove sinθcotθ = cosθ Sinθ x cosθ/sinθ = cosθ SinθCosθ/sinθ = cosθ cos θ = cos θ Prove tan x + cos x=sin x (sec x + cot x) Sinx Secx + sinx cotx = tanx + cosx Sinx * 1/cosx + sinx * cosx/sinx = tanx + cosx sinx/cosx + cosx = tanx + cosx tanx + cosx = tanx + cos x Prove 1 + cosθ = (sin^2)θ/1-cosθ 1-(cos^2)θ / 1-cosθ = 1 + cosθ (1-cosθ)(1+cosθ)/1-cosθ = 1+cosθ 1 + cosθ = 1 + cosθ Prove 1 + sin t/cos t = cos t/1-sin t Cos t (1+sin t)/1-(sin^2) t = 1+sin t/cos t Cos t (1+sin t)/cos^2 t = 1+sin t/cos t 1+sin t/cos t = 1+sin t/cos t Prove tan x + cot x = sec x*cscx sinx/cosx+cosx/sinx = secx*cscx (sin^2)x + (cos^2)x/cosx*sin = secx*cscx 1/cosx*sinx = secx*cscx 1/cosx*1/sinx = secx*cscx secx*cscx = secx*cscx Solve for x (In degrees): 2 sin x-1=0 x = 30 degrees + 360 degrees*k or x = 150 degrees + 360 degrees*k Find all degree solutions to sin (2A – 50 degrees) = (√3)/2 A = 55 degrees + 180 degrees*k or A = 85 degrees +180 degrees*k Solve 2(cos^2) t -9 cos t = 5 if 0≤t≤2π Cos t = -1/2 (t = 2π/3 or 4π/3) or Cos t = 5 (no solution) Solve 3 sin θ – 2 = 7 sin θ -1 if 0 degrees ≤ θ ≤ 360 degrees 194.5 degrees (quadrant III) or 345.5 degrees (quadrant IV) Solve 2sinθ-3 = 0 if 0 degrees ≤ θ ≤ 360 degrees No solution (the sine graph never crosses the x-axis) Make your wager Draw and label the unit circle, with measurements in both radians and degrees. Final Question