Name : ________________________
MHF4U1
Unit 4: Trigonometry Part 1
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KNOWLEDGE/UNDERSTANDING
____ 1. Convert 135 to radians.
a.
[1K]
c.
b.
d.
____ 2. What is the arc length if the central angle is 225 and the radius of a circle is 3 cm?
a. 0.4166 cm
c. 2.4 cm
b. 2.25 cm
d. 3.93 cm
[1K]
____ 3. What is the exact value of sin
[1K]
___
?
a.
c.
b. 0.7071
d.
4. Which value for is a solution to
?
a.
c.
b.
d.
[1K]
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____ 5. Homer Simpson thinks that
is an identity because
following is a counterexample to his claim?
a.
b.
____ 6. If
c.
d.
, what is
, given that
is an identity.
?
a.
c.
b.
d.
[1K]
_____ 7. Which expression is a proper simplification of
?
a.
c.
b.
d.
____ 8. For an acute angle, , of a right triangle,
a possible size for ?
a.
b.
. Which of the
[1K]
[1K]
. Which measurement is
[1K]
c.
d.
2
____ 9. Which expression is equivalent to
a.
b.
?
[1K]
c.
d.
10. Evaluate:
[3K]
sin 5π/4 – (cos 11π/6)(cot π/3)
11. The value of sin  
 25
, where 0    2
26
[5K]
a) In which quadrant(s) could the terminal arm of  lie? Draw a diagram.
b) Determine the reciprocal trigonometric ratios csc  , sec  and cot  .
c) Evaluate all possible values of  , which satisfies the equation.
3
12. Find an equivalent trig expression for cos 2π/9 = 0.766. Provide a diagram which shows
where your equivalent trig expression is located.
[5K]
APPLICATION
1. Use compound angle formulas to calculate the exact value of each expression.
[4A]
CHOOSE ANY TWO FROM THE FOLLOWING:
a) sin 15
b) sin 
7
12

c) cos
4
11
12

 8 
d) sin  
 3 
2. The LADAR satellite is in an orbit 100 km above the Earth’s surface. If the satellite sweeps out
an angle of 225 degrees, find the arc length distance that the satellite has travelled in its orbit.
Draw a diagram of the satellite’s trajectory.
[4A]
Note: The Earth’s radius is Rearth = 6.37 x 106 m.
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3. The old school race track, Mario Circuit #1 (the very first Mario race track!), in Super Mario
Kart 1 is shown below. Each bend has an arc length associated with it, and is labeled as
such. On the final lap, Toad and Yoshi are neck to neck until they reach the last bend
before reaching the finish line. The last bend subtends an angle of 120˚, where the outside
radius (i.e. the distance to the outside edge of the track) measures 33m, and the inside
radius measures 26m.
[4A]
(a) Find the maximum and minimum arc lengths that can be covered by a racer on the last
bend of the track?
(b) If Toad covers the last bend in 57.9m arc length and Yoshi ends up overtaking Toad,
what is the possible range (i.e. within the radius of the bend) that Yoshi could have
taken to overpass Toad? Assume that Vtoad=VYoshi
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COMMUNICATION
1. Why is it useful to apply compound angle formulas to find the exact value of sin 7π/12?
Provide an illustration.
[2C]
2. Explain how an engineer would use arc length to design an appropriate exit ramp off the
highway. Consider the speed in which drivers would enter the exit ramp.
[2C]
THINKING
CHOOSE ANY THREE FROM THE FOLLOWING FIVE QUESTIONS…
1. Using a compound angle formula, demonstrate that
3
3
   2 and
2. Given sin    , where:
5
2
exact values of:
(a)
7
is equivalent to
where 0   

2
. [3T]
. Determine the
[3T]
3. Calculate
if
.
[3T]
4. Determine the value of sin(2θ) when
, and
5. Prove : sin (x+y) / (sinx)(cosy) = 1 + (tany)(cotx)
BONUS QUESTION [+2]
Prove: (sin 2x / sinx) – (cos 2x/cosx) = secx
8
.
[3T]
[3T]
Equivalent Trig Identities
Double Angle Formulas
Compound Angle Formulas
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