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Lesson D - Assignment Booklet

Mathematics 30-1: Unit 2

Back to Baker Street?

Complete the Back to Baker Street assignment. Refer to the Tips From

Scotland Yard located at the back of this lesson booklet to assist you

in completing the assignment. Please show pertinent work and

explanation.

Multiple-Choice Items

1

_________ 1. The statement about identities that is false is

A. the permissible values will always produce identical values on both

sides of the equation

B. the non-permissible values will always produce identical values on

both sides of the equation

C. when graphing each side of an identity, the graphs will be identical

D. substituting in any value for the angle, other than a non-permissible

value, will result in both sides of the equation being equal

2

_________ 2. The expression

cos x is equivalent to

1 - sin x

A. 1 + sin x

cos x

B. 1 - sin x

cos x

C. cos(x)(1 + sin(x))

D. cos(x)(1 ? sin(x))

Numeric Response 1

1

76

Given the domain 0c # i # 360c , the smallest non-permissionable value of the identity

cos?(cos? ? sec?) = cos2? ? 1 is

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Mathematics 30-1: Unit 2

4

Lesson D - Assignment Booklet

_________ 3. The exact value of sin 255° is

A. ^- 3 - 1h

2 2

B.

^ 3 + 1h

C.

^- 3 + 1h

D.

^ 3 - 1h

2 2

2 2

2 2

Numeric Response 2

1

To verify the identity 1 ? sin?cos?tan? = cos2?, a student substituted in ? = 324°. To the

nearest hundredth, the value of each side of the identity is

1

_________ 4. The expression cos(A + ?) ? sin(A + ?) can be simplified to

A. sin(A) ? cos(A)

B. sin(A) + cos(A)

C. cos(A) ? sin(A)

D. ?sin(A) ? cos(A)

Numeric Response 3

2

r

Given sin A = 5 and cos B = 4 , where A and B are both between 0 and 2 then to the

13

5

nearest hundredth, sin(B ? A) =

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77

Lesson D - Assignment Booklet

Mathematics 30-1: Unit 2

Written Response

1.

Given the identity csc i sec i = csc2 i ,

tan i

1

?

State all restrictions on ?

2

?

Verify that the identity is true for i =

1

?

Graph the two sides of the equation on the grid below in the domain

0 &lt; ? &lt; 2?.

78

Alberta Distance Learning Centre

r

, using EXACT values.

4

Mathematics 30-1: Unit 2

2.

Lesson D - Assignment Booklet

Given the equation: (sin(x) + cos(x))2 = sin2(x) + cos2(x),

1

?

State all restrictions on x

2

?

Verify that the equation is identical on each side using x = r .

2

2

?

Determine, giving a reason, whether this is an identity.

Total:

22

Alberta Distance Learning Centre

79

Mathematics 30-1: Unit 2

Lesson D: Trigonometric Identities

S

Standard of Excellence

? Students need to make connections to other courses to complete.

? Successful completion shows an ability to think beyond given examples.

O

Over the acceptable level of understanding

? Students need to make connections from within the course notes and

example to complete.

? Successful completion shows an ability to draw from given instruction and

apply skills to new problems.

L

Level of acceptable standards

? Students need to show acceptable levels of understanding to complete.

? Successful completion shows ability to follow given examples.

V

Below level of acceptable standards

? Student's response to question is below acceptable standard.

E

? Student's response to question indicates student needs assistance in

understanding basic concepts.

80

Alberta Distance Learning Centre

STATUS
QUALITY
Approved

This question was answered on: Feb 21, 2020

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