Chapter 7 Trig Identities

Question 1

Circle

Answer 1

x² + y² = r²

Question 2

Sin θ

Answer 2

y / r

Question 3

Cos θ

Answer 3

x / r

Question 4

Tan θ

Answer 4

y / x or sin θ / cos θ

Question 5

Cos² θ + Sin² θ

Answer 5

1

Question 6

1 + tan² θ

Answer 6

sec² θ

Question 7

1 + cot² θ

Answer 7

csc² θ

Question 8

csc θ

Answer 8

1 / sin θ

Question 9

sin θ

Answer 9

1 / csc θ

Question 10

csc^-1 x

Answer 10

sin^-1 (1/x)

Question 11

sec θ

Answer 11

1 / cos θ

Question 12

cos θ

Answer 12

1 / sec θ

Question 13

sec^-1 x

Answer 13

cos^-1 (1/x)

Question 14

cot θ

Answer 14

1 / tan θ

Question 15

tan θ

Answer 15

1 / cot θ

Question 16

cot^-1 x

Answer 16

tan^-1 (1/x)

Question 17

sin (-θ)

Answer 17

-sin θ

Question 18

tan (-θ)

Answer 18

-tan θ

Question 19

csc (-θ)

Answer 19

-csc θ

Question 20

cot (-θ)

Answer 20

-cot θ

Question 21

cos (-θ)

Answer 21

cos θ

Question 22

sec (-θ)

Answer 22

sec θ

Question 23

sin (A + B)

Answer 23

sin A cos B + cos A sin B

Question 24

cos (A + B)

Answer 24

cos A cos B - sin A sin B

Question 25

tan (A + B)

Answer 25

tan A + tan B / 1 - tan A tan B

Question 26

sin (A - B)

Answer 26

sin A cos B - cos A sin B

Question 27

cos (A - B)

Answer 27

cos A cos B + sin A sin B

Question 28

tan (A - B)

Answer 28

tan A - tan B / 1 + tan A tan B

Question 29

sin 2θ

Answer 29

2 sin θ cos θ

Question 30

cos 2θ

Answer 30

cos²θ - sin²θ, cos²θ - 1, 1 - 2sin²θ

Question 31

tan 2θ

Answer 31

2 tan θ / 1 - tan²θ

Question 32

sin²θ

Answer 32

1 - cos 2θ / 2

Question 33

cos²θ

Answer 33

1 + cos 2θ / 2

Question 34

sin θ/2

Answer 34

±√1 - cos θ / 2

Question 35

cos θ/2

Answer 35

±√1 + cos θ / 2

Question 36

tan θ/2

Answer 36

1 - cos θ / sin θ, sin θ / 1 + cos θ, ±√1 - cos θ / 1 + cos θ