Trigonometry and Differentiation

Question 1

What are the 4 complementary relationship formulas?

Answer 1

sin(Π/2- θ)=cos θ
cos(Π/2- θ)=sin θ
sin(Π/2+ θ)=cos θ
cos(Π/2+ θ)= -sin θ

Question 2

What are the starting y-points for sin graphs and cos graphs?

Answer 2

sin: 0
cos: 1

Question 3

What are the symmetrical properties (due to odd/even functions) of sin (-θ), cos(-θ) and tan(-θ)?

Answer 3

-sinθ
cosθ
-tanθ

Question 4

What are the 3 techniques to consider when dealing with trig equations containing more than one trig equation?

Answer 4

• any common factors which will enable us to factorise?
• any squared signs so we can use sin^2x + cos^2x =1
• is sinx/cosx= tanx helpful?

Question 5

How to find average rate of change for an interval and instantaneous rate of change at a point?

Answer 5

av rate of change: y2-y1/ x2-x1
instant: f’(x)

Question 6

What are the 3 methods of determining the nature of a stationary point?

Answer 6

• Calculate y-coords of points slightly to the left and slightly to the right
• calculate gradient at points slightly to the left and right
• use second derivative

Question 7

Describe what these become on a derivative graph:
stationary point of inflection
non-stationary points of inflection
turning point
what abt gradient?

Answer 7

• stationary point on the x axis
• stationary point not on the x axis
• x axis
  hv positive gradient= derivative graph above x axis
  hv negative gradient= derivative graph below x axis

Question 8

How to use derivatives to determine velocity and acceleration displacement?

Answer 8

Displacement–dif–> velocity –dif–> acceleration

Question 9

What is the derivative of: a(x^n)

Answer 9

an(x^n-1)

Question 10

What is the derivative of: e^kx

Answer 10

ke^kx

Question 11

What is the derivative of: e^f(x)

Answer 11

f’(x) e^f(x)

Question 12

What is the derivative of: k ln x

Answer 12

k/x

Question 13

What is the derivative of: ln kx

Answer 13

1/x

Question 14

What is the derivative of: ln f(x)

Answer 14

f’(x)/ f(x)

Question 15

What is the derivative of: sin kx

Answer 15

k cos kx

Question 16

What is the derivative of: sin f(x)

Answer 16

f’(x) cos f(x)

Question 17

What is the derivative of: cos kx

Answer 17

-k sin kx

Question 18

What is the derivative of: cos f(x)

Answer 18

• f’(x) sin f(x)

Question 19

What is the derivative of: tan kx

Answer 19

k/ cos^2kx

Question 20

What is the derivative of: tan f(x)

Answer 20

f’(x)/ cos^2 f(x)

Question 21

(f(x))^n

Answer 21

n (f(x))^n-1 f’(x)

Question 22

What is the formula for surface area of a cylinder?

Answer 22

2πr^2 + 2πrh

Question 23

What is the formula for surface area of a cone?

Answer 23

πrs+ πr^2

Question 24

What is the formula for volume of a cylinder?

Answer 24

πr^2h

Question 25

What is the formula for volume of a cone?

Answer 25

1/3hπr^2