HCH4: Trigonometric Functions

Question 1

Changing degrees to radians

Answer 1

x˚ x π/180

Question 2

Changing radians to degrees

Answer 2

x x 180˚ / π

Question 3

Arc length of sector

Answer 3

l = rø

Question 4

Radius of sector

Answer 4

r = l ÷ ø

Question 5

Angle of sector

Answer 5

ø = l ÷ r

Question 6

Area of a sector

Answer 6

A = 0.5 r^2 ø

Question 7

Area of a minor segment

Answer 7

A = 0.5 r^2 (ø - sinø)

Question 8

Graphs of trigonometric functions

Answer 8

y = d + acos (bx - C)

vertical shift = d (+ goes up y axis, - goes down x axis)

phase shift = c / b ( + = )

period: 2π / b

interval = period ÷ 4

amplitude = a

Question 9

Special limits

Answer 9

lim sin h = 1
h->0 ———
h

lim cos h = 0
h->0 ———
h

Question 10

Standard trig derivatives

Answer 10

y = cos(ax + b)
y' = -asin(ax+b)

y = sin(ax+b)
y' = a cos(ax + b)

y= tan ax
y' = a sec^2 ax

Question 11

Standard trig integrals

Answer 11

∫ cosx dx = sinx + C
∫ sinx dx = -cosx + C
∫ sec^2x dx = tanx + C