Chapter 18 - Trigonometry 2 (Pure)

Question 1

whats the equation for arc length?

Answer 1

arc length (s) = rΘ

Question 2

whats the equation for area of a sector?

Answer 2

A= 1/2 r Θ²

Question 3

where can you find the small angle approximations?

Answer 3

you can find the small angle approximations in the data sheet

Question 4

what is the domain and range of arcsin? what are the endpoints?

Answer 4

for arcsin limit sins domain to -π/2 and π/2 ( the range stays between -1 and 1 )

so the domain of arcsin x is between -1 and 1
the range of arcsin is now -π/2 and π/2. they flip

the graph goes through the origin

the endpoints of arc sign are (-1,-π/2 ) and (1, π/2)

Question 5

what is the domain and range of arccos? what’s the endpoints?

Answer 5

for arcos limit the domain of cos to 0 to π (the range of cos is still -1 to 1)

therefore domain of arcos is -1 to 1
the range of arcos is 0 to π

the graph cross the y axis at (0,π/2)

the coordinates of its endpoints are (-1, π) and (1,0)

Question 6

what is the domain and range of arctan? what’s the endpoints?

Answer 6

for arctan limit the domain of tanx to -π/2 and π/2 ( the range isn’t limited tho)

this means that the domain of arctan isn’t limited

the range of arctan is -π/2 to π/2

the graph goes through the origin

it has asymptotes no endpoints at y=π/2 and y= -π/2

Question 7

what is cosec?

Answer 7

cosec is 1/sin

Question 8

whta is sec?

Answer 8

sec is 1/ cos

Question 9

what is cot?

Answer 9

cot is 1/tan

cot is cos/ sin

Question 10

what does y=cosec look like? what are the maximum and minimum points?

Answer 10

since cosec x=1/sin x is undefined at any point where sin x= 0

so y=cosec x has vertical asymptotes at x=nπ

the graph y=cosec x has minimum points at x=…, -3/2 π, π/2, 5/2 π ect

the graph has maximum at x=-π/2, 3/2 π, 7/2 π

Question 11

what does y=sec look like? what are the maximum and minimum points?

Answer 11

y=secX is undefined

y=secX has vertical asymptotes at X=(nπ + π/2)

the graph has minimums at x=o, 2π, 4π

it has maximums at x= π, 3π, 5π

Question 12

what does y-=cot x look like? what are the minimums and maximums?

Answer 12

has vertical asymptotes at x=nπ

y=cot x cross the x axis at the same points as a tan graph.

Question 13

what’s ‘sexy tans’?

Answer 13

sec² x = 1 + tan² x

Question 14

what’s ‘cosey cots’?

Answer 14

cosey cots is

1+ cot²x = cosec²x

Question 15

where are the trig identities found?

Answer 15

the trig identities are found on the data sheet.

Question 16

what is the double angle formula for sin2A?

Answer 16

sin 2A = 2sinA cosA

Question 17

what are the double angle formula for cos 2A?

Answer 17

cos 2A= cos²A - sin²A

cos 2A= 2cos²A - 1

cos 2A= 1- 2 sin²A

Question 18

what are the three half angle formula?

Answer 18

cos²(x/2) = 1/2 (1+ cos x)

sin²(x/2) = 1/2 (1 - cos x)

tan²(x/2) = (1 - cos x ) / (1 + cos x )