UNIT 5 test for mathematics calculus

For the angle moving counter-clockwise in standard position, determine which primary trigonometric ratio is positive.. Without using a calculator, determine which ratio is valid.. Withou

UNIT 5 – TEST Student name: _

Identify the choice that best completes the statement or answers the question.

1 Determine the value of to the nearest degree if

2 Determine the corresponding reciprocal ratio that corresponds to

3 Determine the exact value of

4 For the angle moving counter-clockwise in standard position, determine which primary

trigonometric ratio is positive

5 Angle lies in quadrant 4 Without using a calculator, determine which ratio is valid

1)

2)

3)

4)

6 Given , determine which of the following is an equivalent expression

7 A triangular plot of land is enclosed by a fence One side of the fence is 40.1 m long with an opposite angle

of An adjacent side of the fence is 37.7 m long with an opposite angle of Determine to the nearest degree

8 Order the following waves according to the length of their periods, from least to greatest.

Wave A

Wave B

Wave C

1

2

3

4

5

–1

–2

–3

–4

y

a Wave B, Wave A, Wave C c Wave C, Wave B, Wave A

b Wave C, Wave A, Wave B d Wave B, Wave C, Wave A

9 If , determine

10 Determine the amplitude of the function

11 Determine the period of the function

12 Determine the period of graph A and graph B

A

B

–1 –2 –3 –4

1 2 3 4 5

–1 –2 –3 –4 –5

y

13 Without graphing, determine the equation of the axis of the function

b d.

14 State the order of transformations for the function

a horizontal transformation left ; vertical stretch by a factor of 0.125

b horizontal transformation left ; vertical compression by a factor of 0.125

c horizontal transformation right ; vertical stretch by a factor of 1

d horizontal transformation right ; vertical compression by a factor of 1

15 Which of the following does not make sense?

a

period of

c amplitude of

b vertical stretch by a factor of 0.005 d horizontal translation 3 units left

Question # 1 2 3 4 5 6 7 8

Answer

Answer

Short Answer

16 For the function

2 ) 5 22 2

1 ( sin 2

5

−

°

−

−

y

, State the transformations, in the order you would apply them (C: /3)

_

_

17 Determine one value for which is true and one value for which it is not true (C: /2)

18 If you are given 3 sides of a triangle, how can you find the measure of its angles? (C: /2)

19 Fill in the following table for y = 5cos (3x + 180°) + 1 and sketch 3 cycles of the function (A: /8)

20 A scientist records the motion of a particle where d is the

distance in mm and t is the time in seconds A graph of

that motion is shown below.

(A: /4)

a)What is the period of one complete cycle?

b) What is the range of this function?

c) Determine the amplitude

d) If the particle can survive for twenty complete cycles before deteriorating, determine the domain

of the function

21 How many triangles can you make if in ∆XYZ

,

42.6o Y

∠ =

, y = 6.9 m, z = 9.7 m?

(A: _/3)

22 Prove the following identity: (T: _/4)

a)

θ θ

θ θ

θ

cos sin cos

sin cos

2

2 2

−

= +

−

23 The Ferris wheel at a carnival has a diameter of 10 m and rotates once every 40 seconds The bottom of the wheel is 2m above the ground Draw a diagram to show a rider’s height above the ground during 1 ride, starting at the lowest position (T: /4)

a find the equation of the sine function that gives a rider’s height above the ground, in meters, as a

function of the time, in seconds (T: /2)

Equation:

b Suppose the Ferris wheel rotates every 10 seconds Adjust your equation in part a) to reflect this

new situation (T: /1)

Equation:

c) Using the same situation as part a, model the rider’s height using a cosine function. (T: /2)

Equation: