Trigonometry 1 Test on Thursday March 16, 2017

Question 1

Find a positive and a negative angle co-terminal with a 55° angle.

Answer 1

55° − 360° = −305°

55° + 360° = 415°

Question 2

Without a calculator, explain the difference between the equation and expression below.

cosΘ = 0

and

cos0°

Answer 2

cosΘ = 0

We need to solve for the angle

=================

Θ = 90° and 270°

cos0°

We have to solve for cos of 0°

We need to solve the x coordinate of the angle

======================

Question 3

Which of the following is true about Quadrant IV?

A.) tanΘ < 0 and sin < 0
B.) tanΘ > 0 and sin < 0
C.) tanΘ < 0 and sin > 0

Answer 3

A.) tanΘ < 0 and sin < 0

tan is negative in QIV

sin is negative in QIV

Question 4

Which of the following statement is false?

The unit circle has:

a) Centre (0,0)
b) Diameter of π/2
c) Radius of 1
d) Circumference, around a circle is 2π

Answer 4

b) Diameter of π/2

Question 5

Define Coterminal angle

Answer 5

Coterminal angles are angles in standard position (angles with the initial side on the positive xx -axis) that have a common terminal side. For example 30°30° , −330°−330° and 390°390° are all coterminal.

Question 6

iN TERMS OF COS, RANK THE FOLLOWING FROM BIGGEST TO SMALLEST

√2/2

0

1

1/2

√3/2

Answer 6

1

√3/2

√2/2

1/2

0

Question 7

What is the coefficient of π for 360°?

Answer 7

2π

Question 8

iN TERMS OF sin, RANK THE FOLLOWING FROM BIGGEST TO SMALLEST

Answer 8

0

1/2

√2/2

√3/2

1

Question 9

iN TERMS OF COS, RANK THE FOLLOWING FROM SMALLEST TO BIGGEST

Answer 9

0

1/2

√2/2

√3/2

1

Question 10

iN TERMS OF sin, RANK THE FOLLOWING FROM SMALLEST TO BIGGEST

Answer 10

1

√3/2

√2/2

1/2

0

Question 11

When tanΘ is ±√1/8, how many solutions are there given the restriction,

Answer 11

4

Question 12

Given 30°, what is it’s cos, sin and tan values?

Answer 12

cos: √3/2 (Remember: cos = x)
sin: 1/2 (Remember: sin = y)
tan: 1/√3 or √3/3 (Remember: tan = y/x)

Question 13

Given 0°, what is it’s cos, sin and tan values?

Answer 13

cos: 1 (Remember: cos = x)
sin: 0 (Remember: sin = y)
tan: 0 (not undefined because it is not vertical)

Question 14

Given 90°, what is it’s cos, sin and tan values?

Answer 14

cos: 0 (Remember: cos = x)
sin: 1 (Remember: sin = y)
tan: undefined (because it is vertical)

Question 15

Given 45°, what is it’s cos, sin and tan values?

Answer 15

cos: √2/2 (Remember: cos = x)
sin: √2/2 (Remember: sin = y)
tan: 1 (Remember: tan = y/x)

Question 16

Given 60°, what is it’s cos, sin and tan values?

Answer 16

cos: 1/2 (Remember: cos = x)
sin: √3/2 (Remember: sin = y)
tan: √3 (Remember: tan = y/x)

Question 17

Given 225°, what is it’s cos, sin and tan values?

Answer 17

cos: -√2/2 (Remember: cos = x)
sin: -√2/2 (Remember: sin = y)
tan: 1 (Remember: tan = y/x)

Question 18

Given 330°, what is it’s cos, sin and tan values?

Answer 18

cos: √3/2 (Remember: cos = x)
sin: -1/2 (Remember: sin = y)
tan: -1/√3 (Remember: tan = y/x)

Question 19

Given 150°, what is it’s cos, sin and tan values?

Answer 19

cos: -√3/2 (Remember: cos = x)
sin: 1/2 (Remember: sin = y)
tan: -1/√3 (Remember: tan = y/x)

Question 20

Given 135°, what is it’s cos, sin and tan values?

Answer 20

cos: -√2/2 (Remember: cos = x)
sin: √2/2 (Remember: sin = y)
tan: -1 (Remember: tan = y/x)

Question 21

Given 240°, what is it’s cos, sin and tan values?

Answer 21

cos: -1/2 (Remember: cos = x)
sin: -√3/2 (Remember: sin = y)
tan: (Remember: tan = y/x)

Question 22

Given 300°, what is it’s cos, sin and tan values?

Answer 22

cos: 1/2 (Remember: cos = x)
sin: -√3/2 (Remember: sin = y)
tan: (Remember: tan = y/x)

Question 23

Given 270°, what is it’s cos, sin and tan values?

Answer 23

cos: 0 (Remember: cos = x)
sin: -1 (Remember: sin = y)
tan: undefined (because it is vertical)

Question 24

What is the formula of tan? (not TOA)

Answer 24

y/x

Question 25

What is sin?

Answer 25

y

Question 26

what is cos?

Answer 26

x

Question 27

Given the restriction, 0° < Θ < 90°, what is the quadrant?

Answer 27

Quadrant I

Question 28

Given the restriction, 90° < Θ < 180°, what is the quadrant?

Answer 28

Quadrant II

Question 29

Given the restriction, 180° < Θ < 270°, what is the quadrant?

Answer 29

Quadrant III

Question 30

Given the restriction, 270° < Θ < 360°, what is the quadrant?

Answer 30

Quadrant IV

Question 31

If you were given angle, let’s say 53°, how do you find another angle, let’s say with the same cos value?

Answer 31

You use Add Sugar To Coffee or All Snow Taste Cold and find you other values.