P- Arc length, sector area, sin, cos, tan, radians & small angle approximations- DF

Question 1

For Sine, when will it be positive and when will it be negative?

Answer 1

= θ = POS
= 180-θ = POS
= 180+θ = NEG
=360-θ = NEG

Question 2

For Cos, when will it be positive and when will it be negative?

Answer 2

= θ = POS
= 180-θ = NEG
= 180+θ = NEG
= 360-θ = POS

Question 3

For Tan, when will it be positive and when will it be negative?

Answer 3

= θ = POS
= 180-θ = NEG
= 180+θ = POS
= 360-θ = NEG

Question 4

How many radians are in 90, 180, 270 and 360 degrees?

Answer 4

90 = 0.5 π radians
180 = π radians
270 = 3 π/2 radians
360 = 2 π radians

Question 5

What is the asyptote?

Answer 5

On a tan graph, the dotted line which the solid ones never touch

Question 6

What is a radian?

Answer 6

The angle that gives an arc length equal to the radius

Question 7

How are radians given?

Answer 7

In terms of pi

Question 8

What does multiplying in and out a function do?

Answer 8

Inside = x direction stretch only
Outside = y direction stretch only

Question 9

What does adding inside and outside the function do?

Answer 9

Inside = translates left along the x axis
Outside = translates upwards along the y axis

Question 10

What does subtracting inside and outside the function do?

Answer 10

Inside = translation along the x axis to the right
Outside = translation along the y axis downwards

Question 11

What is the formula for sector area in degrees and radians?

Answer 11

Degrees= r2 π x 360/θ
Radians= 0.5 x r2 x θ

Question 12

What is the arc length formula in degrees and radians?

Answer 12

Degrees= 2πr x theta/360
Radians= r θ

Question 13

In radians, when the angle is small, what is Sinθ ?

Answer 13

θ

Question 14

In radians, when the angle is small, what is Tanθ ?

Answer 14

θ

Question 15

In radians, when the angle is small, what is Cosθ ?

Answer 15

1- θ squared ÷ 2