Download Trig Chapter 4 and 5

TRIGNOMETRIC FUNCTIONS AND THE UNIT CIRCLE
DIPLOMA STYLE QUESTIONS
1. The angle
15
converted to degrees, is:
4
2. An angle, in radians, that is co-terminal with 30⁰ is
A. 
5
6
B. 
13
6
C.
7
6
D.
25
6
Use the following information to answer the next question.
An angle, θ, in standard position is shown below.
θ
3. The best estimate of the rotation of angle θ is
A. 1.25 radians
B. 3.12 radians
C. 4.01 radians
D. 5.38 radians
Use the following information to answer the next question.
Mary is given the diagram below, showing an angle rotation of 120⁰. The arc length of
the sector is 40 cm.
40 cm
120⁰
Statement 1
The radius of the circle, to the nearest centimeter, is 19 cm.
Statement 2
An equivalent angel rotation is
Statement 3
If the arc length on this circle increases to 80 cm, then the central angle
must be 240⁰.
Statement 4
Mary can determine the radius of the circle by dividing the given angle
by the arc length.
4𝜋
.
3
4. The two statements above that are correct are numbered _______ and _______.
5. On a unit circle, if the point P(-
5 12
, )
13 13
lies on the terminal arm of an angle in standard position, what
are the exact values of the 6 trigonometric ratios?
8
3𝜋
6. Given that csc θ= - 5, where π < θ < 2 , determine the exact value of tan θ
𝜋
7. Determine the exact value of sin (- 6 ) + cos (
7𝜋
4
). (SE)
Use the following information to answer the next question.
𝑎𝜋
A circle with a radius, r, an arc length of 34π, and two central angles of 15 and
17𝜋
15
is shown
below.
𝑎𝜋
15
17𝜋
15
34π
The value of a in the angle
𝑎𝜋
15
is bc.
The length of the radius, r, of the circle, to the nearest whole number, is de.
8. The values of b, c, d and e are, respectively, _________, _________, _________, and _________.
Use the following information to answer the next question.
If the point P(0.2, k) lies on a circle with a radius of 1, then the exact value of k can
be expressed as ±√𝑏.
9. The value of b, to the nearest hundredth, is ___________.
5
2
10. If tan θ = , where 0 ≤ θ ≤ 2π, then the largest positive value of θ, to the nearest tenth is _______ rad.
Use the following information to answer the next question.
√3 1
Point A ( 2 , 2) and point B (-
√2 √2
, )
2 2
lie on the terminal arm of two different angles in
standard position. The angle, θ, where 0 < θ <π, can be expressed in the form
B
𝑎𝜋
.
𝑏
θ
A
11. The values of a and b are, respectively, ________ and ________.
Use the following information to answer the next question.
Each of the trigonometric ratios listed below results in a value of zero, or it will be undefined.
𝜋
2
tan ( )
3𝜋
cot ( 2 )
sin (π)
csc (2π)
12. Use the following code to indicate that the value of the ratio is zero, or that the ratio is undefined.
1 – the value of the ratio is zero.
2 – the ratio is undefined.
____________
Ratio:
𝜋
tan (2 )
____________
3𝜋
cot ( 2 )
____________
sin (π)
____________
csc(2π)
Use the following information to answer the next question.
𝜋 5𝜋 7𝜋 11𝜋
, , 6 ,
6 6
For the angles 6 ,
the following statements are given:
Statement 1
They all have the same reference angle.
Statement 2
These angles in degrees are, respectively 30⁰, 150⁰, 210⁰, and 300⁰.
Statement 3
They are all part of the solution set θ = 6 + 2πn, nєI.
Statement 4
The values of sin (6 ) and sin ( 6 ) are positive.
𝜋
𝜋
5𝜋
13. The two statements that are true from the list above are numbered _______ and _______.
14. For the functions y = acosθ + d, the range is [-4, 10]. What are the values of a and d?
15. For the functions y = sin(3x + π) + 7, what is the phase shift and the period of the corresponding
graph?
16. Given that f(θ) = cos(nθ) has the same period as the graph of g(θ) = tan(θ), the value of n is:
Use the following information to answer the next question.
𝜋
2
The partial graph of the cosine function below has a minimum point at ( , -2) and a maximum point at
(π, 8). The equation of the function can be expressed in the form y = acos(bx) + d.
Y
X
17. What are the values of a, b, and d respectively?
Use the following information to answer the next question.
For the graph of the function f(x) = -3sin[2(x - 5)] + d the following statements were made.
Statement 1
The amplitude is 3.
Statement 2
The maximum value is (d – 3).
Statement 3
When compared to the graph of g(x) = -3sin(2x) + d, the graph of y = f(x) has
been horizontally translated 5 units to the right.
Statement 4
If d < 3, then the graph of y = f(x) will have no x-intercepts.
18. The number of true statements about the graph of y = f(x) from the list above is
A.
1
B.
2
C.
3
D.
4
Use the following information to answer the next question.
The graph below shows the height of a point on a Ferris wheel, h, in meters above the
ground as a function of time, t, in seconds. The maximum height of the Ferris wheel is
17 m and the minimum height is 1 m.
Y
X
19. Write an equation for the height of the particular point on the Ferris wheel, h, as a function of time, t,
in the form h = acos[b(t – c)] + d.