Trigonometry

Question 1

What is the formula for sin(A + B)?

Answer 1

sin(A + B) = sin A . cos B + cos A . sin B

Question 2

What is the formula for sin(A - B)?

Answer 2

sin(A - B) = sin A . cos B - cos A . sin B

Question 3

What is the formula for cos(A + B)?

Answer 3

cos(A + B) = cos A . cos B - sin A . sin B

Question 4

What is the formula for cos(A - B)?

Answer 4

cos(A - B) = cos A . cos B + sin A . sin B

Question 5

What is the formula for tan(A + B)?

Answer 5

tan(A + B) = (tan A + tan B)/(1 - tan A . tan B)

Question 6

What is the formula for tan(A - B)?

Answer 6

tan(A - B) = (tan A - tan B)/(1 + tan A . tan B)

Question 7

Sinθ = ?

Answer 7

Sinθ = 1/cosecθ

Question 8

Cosθ= ?

Answer 8

Cosθ= 1/secθ

Question 9

Tanθ= ?

Answer 9

Tanθ= 1/cotθ ,
sinθ/cosθ

Question 10

Cotθ= ?

Answer 10

Cotθ= 1/tanθ,
cosθ/sinθ

Question 11

Secθ= ?

Answer 11

Secθ= 1/cosθ

Question 12

Cosecθ= ?

Answer 12

Cosecθ= 1/sinθ

Question 13

Sin^2θ+cos^2θ=?

Answer 13

Sin^2θ+cos^2θ=1

Question 14

Sin^2θ=?

Answer 14

Sin^2θ = 1 - cos^2θ

Question 15

cos^2θ=?

Answer 15

cos^2θ= 1 - Sin^2θ

Question 16

1 + tan^2θ = ?

Answer 16

1 + tan^2θ = sec^2θ

Question 17

sec^2θ - tan^2θ = ?

Answer 17

sec^2θ - tan^2θ = 1

Question 18

tan^2θ = ?

Answer 18

tan^2θ = sec^2θ - 1

Question 19

1 + cot^2θ = ?

Answer 19

1 + cot^2θ = cosec^2θ

Question 20

cosec^2θ - cot^2θ = ?

Answer 20

cosec^2θ - cot^2θ = 1

Question 21

cot^2θ = ?

Answer 21

cot^2θ = cosec^2θ - 1

Question 22

Sin(-θ) = ?
Cos(-θ) = ?
Tan(-θ) = ?
Cot(-θ) = ?
Sec(-θ) = ?
Cosec(-θ) = ?

Answer 22

Sin(-θ) = - sinθ
Cos(-θ) = cosθ
Tan(-θ) = - tan θ
Cot(-θ) = - cotθ
Sec(-θ) = secθ
Cosec(-θ) = - cosecθ

Question 23

sin (90-θ) = ?

cos(90-θ ) = ?

tan(90-θ ) = ?

cot(90-θ ) = ?

sec(90-θ) = ?

cosec(90-θ) = ?

Answer 23

sin (90-θ) = cosθ

cos(90-θ ) = sinθ

tan(90-θ ) = cotθ

cot(90-θ ) = tanθ

sec(90-θ) = cosecθ

cosec(90-θ) = secθ

Question 24

cot(A + B) = ?

Answer 24

cot(A + B) = cot B. cot A -1 / cotA+cotB

Question 25

cot(A - B) = ?

Answer 25

cot(A - B) = cot B . cotA + 1 / cotB - cotA

Question 26

sin C + sin D = ?

Answer 26

sin C + sin D = 2 sin (C+D)/2) . cos (C-D)/2)

Question 27

sin C - sin D = ?

Answer 27

sin C - sin D = 2 cos (C+D)/2) . Sin (C-D)/2)

Question 28

cos C + cos D = ?

Answer 28

cos C + cos D = 2 cos (C+D)/2) . cos (C-D)/2)

Question 29

cos C - cos D = ?

Answer 29

cos C - cos D = - 2 sin (C+D)/2) . sin (C-D)/2)

Question 30

sin2x = ?

Answer 30

sin2x = 2sin x . cos x = (2tan x) / (1 + tan^2 x)

Question 31

cos2x = ?

Answer 31

cos2x = ♦ cos^2x - sin^2x = 2cos^2x - 1 ♦ 1 - 2sin^2 x = (1 - tan^2x) / (1 + tan^2 x)

Question 32

tan2x = ?

Answer 32

tan2x = (2tan x) / (1 - tan^2 x)

Question 33

sin3x = ?

Answer 33

sin3x = 3 sin x - 4 sin^3 x

Question 34

Sin(A+B) sin(A-B) = ?

Answer 34

Sin(A+B) sin(A-B) = ♥= sin^2A - sin^2B ♥=cos^2B - cos^2A

Question 35

Cos(A+B) cos(A-B) = ?

Answer 35

Cos(A+B) cos(A-B) = ♥= cos^2A - sin^2B ♥= cos^2B - sin^2A

Question 36

What is the value of sin 15°?

Answer 36

(√3 - 1) / (2√2)

Question 37

What is the relationship between sin 15° and cos 75°?

Answer 37

sin 15° = cos 75°

Question 38

Fill in the blank: sin 15° = _______.

Answer 38

(√3 - 1) / (2√2)

Question 39

True or False: sin 15° is equal to cos 75°.

Answer 39

True

Question 40

What is the value of cos 15°?

Answer 40

(√3 + 1) / (2√2)

Question 41

What is the relationship between cos 15° and sin 75°?

Answer 41

cos 15° = sin 75°

Question 42

Fill in the blank: cos 15° = _______.

Answer 42

(√3 + 1) / (2√2)

Question 43

True or False: cos 15° is equal to sin 75°.

Answer 43

True

Question 44

• sin 18°=

Answer 44

• sin 18°= (√5 - 1) / 4 = Also equal to cos 72°

Question 45

• cos 18° =

Answer 45

• cos 18° = √ ( 10 + 2√5 ) / 4 = Also equal to sin 72°

Question 46

• sin 36°=

Answer 46

• sin 36°= √ (10 - 2√5 ) / 4 = Also equal to cos 54°

Question 47

• cos 36° =

Answer 47

• cos 36° = (√5 + 1) / 4 = Also equal to sin 54°