Chapter 7 Key Equations

Question 1

cos(-x) =

Answer 1

cosx

Question 2

cot(-x) =

Answer 2

-cotx

Question 3

sin(-x)=

Answer 3

-sinx

Question 4

tan(-x)=

Answer 4

-tan(x)

Question 5

cos^2x + sin^2x =

Answer 5

1

Question 6

1 + tan^2x =

Answer 6

sec^2x

Question 7

cot^2x + 1 =

Answer 7

csc^2x

Question 8

cot^2x =

Answer 8

csc^2x - 1

Question 9

tan^2x - sec^2x =

Answer 9

-1

Question 10

tanx =

Answer 10

sinx/cosx

Question 11

cotx =

Answer 11

cosx/sinx

Question 12

sin(a+B) =

Answer 12

sinacosB + cosasinB

Question 13

cos(a+B) =

Answer 13

cosacosB - sinasinB

Question 14

tan(a+B) =

Answer 14

tan(a) + tan(B) / 1 - tan(a)tan(B)

Question 15

sin(t)

Answer 15

cos(π/2 - t)

Question 16

cos(t)

Answer 16

sin(π/2 - t)

Question 17

sin2x =

Answer 17

2sinxcosx

Question 18

cos2x =

Answer 18

cos^2x-sin^2x

Question 19

2cos^2x-1

Answer 19

cos2x

Question 20

1 - 2sin^2x

Answer 20

= cos2x

Question 21

sin^2x =

Answer 21

1 - cos2x / 2

Question 22

cos^2x =

Answer 22

1 + cos2x / 2

Question 23

sin x/2 =

Answer 23

± √1-cosx / 2

Question 24

cos x/2 =

Answer 24

± √1+cosx / 2

Question 25

sinxsiny =

Answer 25

1/2[cos(x-y)-cos(x+y)]

Question 26

cosxcosy =

Answer 26

1/2[cos(x-y)+cos(x+y)]

Question 27

sinxcosy =

Answer 27

1/2[sin(x+y)+sin(x-y)]

Question 28

cosxsiny =

Answer 28

1/2[sin(x+y)-sin(x-y)]

Question 29

sinx + siny =

Answer 29

2sin(x+y/2)cos(x-y/2)

Question 30

sinx - siny =

Answer 30

2cos(x+y/2)sin(x-y/2)

Question 31

cosx + cosy =

Answer 31

2cos(x+y/2)cos(x-y/2)

Question 32

cosx - cosy =

Answer 32

-2sin(x+y/2)sin(x-y/2)