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Final Jeopardy
Graphing
Inverse Trig
Functions
Word
Problems
Trig
Identities
Solving
Equations
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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