adicione formule

Question 1

Šta je osnovna trigonometrijska formula?

Answer 1

sin² x + cos² x = 1

Question 2

Kako se definiše tangens?

Answer 2

tg x = sin x / cos x; x ≠ kπ

Question 3

Kako se definiše kotangens?

Answer 3

ctg x = cos x / sin x; x ≠ kπ

Question 4

Koje su periodične funkcije za sinus?

Answer 4

sin(360°k + x) = sin x

Question 5

Koje su periodične funkcije za kosinus?

Answer 5

cos(360°k + x) = cos x

Question 6

Koje su periodične funkcije za tangens?

Answer 6

tg(180°k + x) = tg x

Question 7

Koje su periodične funkcije za kotangens?

Answer 7

ctg(180°k + x) = ctg x

Question 8

Kako se ponaša sinus kod negacije?

Answer 8

sin(-x) = -sin x

Question 9

Kako se ponaša kosinus kod negacije?

Answer 9

cos(-x) = cos x

Question 10

Kako se ponaša tangens kod negacije?

Answer 10

tg(-x) = -tg x

Question 11

Kako se ponaša kotangens kod negacije?

Answer 11

ctg(-x) = -ctg x

Question 12

Koja je adicija formula za sinus?

Answer 12

sin(x ± y) = sin x cos y ± cos x sin y

Question 13

Koja je adicija formula za kosinus?

Answer 13

cos(x ± y) = cos x cos y ∓ sin x sin y

Question 14

Kako se definiše tangens za zbir?

Answer 14

tg(x ± y) = (tg x ± tg y) / (1 ∓ tg x tg y)

Question 15

Kako se definiše kotangens za zbir?

Answer 15

ctg(x ± y) = (ctg x ctg y ∓ 1) / (ctg x ± ctg y)

Question 16

What is the formula for sin 2x?

Answer 16

sin 2x = 2 sin x cos x

This formula is derived from the double angle identities for sine.

Question 17

What is the formula for cos 2x?

Answer 17

cos 2x = cos² x - sin² x

This is another expression of the double angle identity for cosine.

Question 18

What is the formula for tg 2x?

Answer 18

tg 2x = (2 tg x) / (1 - tg² x)

This formula provides a way to express the tangent of a double angle.

Question 19

What is the half-angle formula for sin?

Answer 19

sin(x/2) = √((1 - cos x) / 2)

This formula allows one to find the sine of half an angle using the cosine of the full angle.

Question 20

What is the half-angle formula for cos?

Answer 20

cos(x/2) = √((1 + cos x) / 2)

This formula allows one to find the cosine of half an angle using the cosine of the full angle.

Question 21

What is the formula for sin 3x?

Answer 21

sin 3x = 3 sin x - 4 sin³ x

This formula is derived from the trigonometric identity for sine of a triple angle.

Question 22

What is the formula for cos 3x?

Answer 22

cos 3x = 4 cos³ x - 3 cos x

This formula is derived from the trigonometric identity for cosine of a triple angle.

Question 23

What is the transformation formula for sin x sin y?

Answer 23

sin x sin y = 1/2 (cos(x - y) - cos(x + y))

This formula is useful for transforming products of sine functions into sums.

Question 24

What is the transformation formula for sin x cos y?

Answer 24

sin x cos y = 1/2 (sin(x - y) + sin(x + y))

This formula facilitates the conversion of sine and cosine products into sums.

Question 25

What is the transformation formula for cos x cos y?

Answer 25

cos x cos y = 1/2 (cos(x - y) + cos(x + y)) ## Footnote This formula is used to rewrite products of cosine functions as sums.

Question 27

What is the formula for sin(x + y)?

Answer 27

sin(x + y) = sinx cosy + siny cosx

Question 28

What is the formula for sin(x - y)?

Answer 28

sin(x - y) = sinx cosy - siny cosx

Question 29

What is the formula for cos(x + y)?

Answer 29

cos(x + y) = cosx cosy - sinx siny

Question 30

What is the formula for cos(x - y)?

Answer 30

cosx cosy + sinx siny

Question 31

What is the relationship between tg(x) and tg(y) in the product form?

Answer 31

tg(x) tg(y) = sin(x + y) / cos(x) cos(y) ## Footnote This represents the tangent of the sum of angles.

Question 32

What is the formula for ctg(x + y)?

Answer 32

ctg(x + y) = sin(x) sin(y) ## Footnote This is the relationship for the cotangent of the sum of angles.

Question 33

What is the value of sin(200)?

Answer 33

Value is not specified ## Footnote This might refer to a specific trigonometric calculation or example.

Question 34

Fill in the blank: sin(x + y) = _______

Answer 34

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

Question 35

Fill in the blank: cos(x + y) = _______

Answer 35

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

Question 36

True or False: sin(x - y) can be expressed as 2 cos((x + y)/2) sin((x - y)/2)

Answer 36

True