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 the identity relating sec and tan?

Answer 13

sec² x = 1 + tan² x

Question 14

what’s the identity relating cot and cosec?

Answer 14

1+ cot²x = cosec²x

Question 15

what is the double angle formula for sin2A?

Answer 15

sin 2A = 2sinA cosA

Question 16

what are the double angle formula for cos 2A?

Answer 16

cos 2A= cos²A - sin²A

cos 2A= 2cos²A - 1

cos 2A= 1- 2 sin²A

Question 17

what are the three half angle formula?

Answer 17

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 )

Question 18

What are the common trigonometric values of this table?

Answer 18