Trigonometry

Question 1

sin30

Answer 1

1/2

Question 2

cos30

Answer 2

root3/2

Question 3

tan30

Answer 3

1/root3

Question 4

sin45

Answer 4

1/root2

Question 5

cos45

Answer 5

1/root2

Question 6

tan45

Answer 6

1

Question 7

sin60

Answer 7

root3/2

Question 8

cos60

Answer 8

1/2

Question 9

tan60

Answer 9

root3

Question 10

tanx

Answer 10

sinx/cosx

Question 11

cotx

Answer 11

cosx/sinx

Question 12

sin^2x+cos^2

Answer 12

=1

Question 13

1+cot^2

Answer 13

=cosec^2x

Question 14

1+tan^2x

Answer 14

=sec^2x

Question 15

cosine rule

Answer 15

c^2 = a^2 + b^2 − 2ab cos(C)

cos(c) =( a^2 + b^2 −c^2) / 2ab

Question 16

angle size (radians)

Answer 16

arc length / radius

Question 17

area of a sector

Answer 17

r^2 theta /2

Question 18

area of minor segment

Answer 18

r^2/2 (theta - sintheta)

Question 19

small angles

Answer 19

sinx ~x
tanx~ x
cosx ~ 1

Question 20

ambiguous case sine rule

Answer 20

if (180 - angle) + given angle < 180

Question 21

differentiating trig

Answer 21

f'(sinx) = cosx 
f'(cosx) = - sinx
f'(tanx) = sec^2x
f'(secx) = secxtanx
f'(cosecx) = -cosecxcotx
f'(cotx) = - cosec^2x

Question 22

integrating trig

Answer 22

sin x dx =  − cos x + C
cos x dx = sin x + C
tan x dx = − ln |cos x |+ C
sec^2x dx = tan x + C
cosec^2x dx =  − cot x + C
cosecx cotx = -cosecx

Question 23

cos2x

Answer 23

cos^2x - sin^2x
2cos^2x-1
1-2sin^2x

Question 24

sin2x

Answer 24

2sinxcosx

Question 25

sec^2x

Answer 25

1+tan^2x

Question 26

cosec^2x

Answer 26

1+cot^2

Question 27

cos^2x-sin^x

Answer 27

cos2x

Question 28

2cos^2x-1

Answer 28

cos2x

Question 29

1-2sin^2x

Answer 29

cos2x

Question 30

2sinxcosx

Answer 30

sin2x