unit 5 formulas

Question 1

sin^2x + cos^2x = ?

Answer 1

1

Question 2

sin^2x = ?

Answer 2

1 - cos^2x

Question 3

cos^2x = ?

Answer 3

1 - sin^2x

Question 4

sec^2x - tan^2x = ?

Answer 4

1

Question 5

sec^2x = ?

Answer 5

1 + tan^2x

Question 6

tan^2x = ?

Answer 6

sec^2x - 1

Question 7

csc^2x - cot^2x = ?

Answer 7

1

Question 8

csc^2x = ?

Answer 8

1 + cot^2x

Question 9

cot^2x = ?

Answer 9

csc^2x - 1

Question 10

sin (a + b)

Answer 10

sin a cos b + cos a sin b

Question 11

sin (a - b)

Answer 11

sin a cos b - cos a sin b

Question 12

cos (a + b)

Answer 12

cos a cos b - sin a sin b

Question 13

cos (a - b)

Answer 13

cos a cos b + sin a sin b

Question 14

tan (a + b)

Answer 14

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

Question 15

tan (a - b)

Answer 15

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

Question 16

sin 2x

Answer 16

2 sin x cos x

Question 17

cos 2x (variation 1)

Answer 17

cos^2x - sin^2x

Question 18

cos 2x (variation 2)

Answer 18

2cos^2x - 1

Question 19

cos 2x (variation 3)

Answer 19

1 - 2sin^2x

Question 20

tan 2x

Answer 20

(2 tan x) / 1 - tan^2x

Question 21

sin^2x

Answer 21

(1 - cos 2x) / 2

Question 22

cos^2x

Answer 22

(1 + cos 2x) / 2

Question 23

tan^2x

Answer 23

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

Question 24

for half angle identities, how do you decide if the square root is positive or negative

Answer 24

see what quadrant x/2 is in, and see if the sin/cos/tan whatever of x/2 is positive or negative

Question 25

sin(x/2)

Answer 25

+/- sqrt((1 - cos x) / 2)

Question 26

cos(x/2)

Answer 26

+/- sqrt((1 + cos x) / 2)

Question 27

tan(x/2)

Answer 27

+/- sqrt((1- cos x) / (1 + cos x))