Тригонометрия

Question 1

sin^2(a) + cos^2(a)

Answer 1

1

Question 2

tg(a)

Answer 2

sin(a) / cos(a)

Question 3

sin(a) / cos(a)

Answer 3

tg(a)

Question 4

ctg(a)

Answer 4

cos(a) / sin(a)

Question 5

cos(a) / sin(a)

Answer 5

ctg(a)

Question 6

tg(a) * ctg(a)

Answer 6

1

Question 7

1 +tg^2(a)

Answer 7

1 / ( cos^2(a) )

Question 8

1 / ( cos^2(a) )

Answer 8

1 +tg^2(a)

Question 9

1 + ctg^2(a)

Answer 9

1 / ( sin^2(a) )

Question 10

1 / ( sin^2(a) )

Answer 10

1 + ctg^2(a)

Question 11

sin(a) + sin(b)

Answer 11

2sin( (a+b)/2 )cos( (a-b)/2 )

Question 12

2sin( (a+b)/2 )cos( (a-b)/2 )

Answer 12

sin(a) + sin(b)

Question 13

sin(a) - sin(b)

Answer 13

2cos( (a+b)/2 )sin( (a-b)/2 )

Question 14

2cos( (a+b)/2 )sin( (a-b)/2 )

Answer 14

sin(a) - sin(b)

Question 15

cos(a) + cos(b)

Answer 15

2cos( (a+b)/2 )cos( (a-b)/2 )

Question 16

2cos( (a+b)/2 )cos( (a-b)/2 )

Answer 16

cos(a) + cos(b)

Question 17

cos(a) - cos(b)

Answer 17

-2sin( (a+b)/2 )sin( (a-b)/2 )

Question 18

-2sin( (a+b)/2 )sin( (a-b)/2 )

Answer 18

cos(a) - cos(b)

Question 19

tg(a) + tg(b)

Answer 19

sin(a+b) / ( cos(a)*cos(b) )

Question 20

sin(a+b) / ( cos(a)*cos(b) )

Answer 20

tg(a) + tg(b)

Question 21

tg(a) - tg(b)

Answer 21

sin(a-b) / ( cos(a)*cos(b) )

Question 22

sin(a-b) / ( cos(a)*cos(b) )

Answer 22

tg(a) - tg(b)

Question 23

sin(a+b)

Answer 23

sin(a)cos(b) + cos(a)sin(b)

Question 24

sin(a)cos(b) + cos(a)sin(b)

Answer 24

sin(a+b)

Question 25

sin(a-b)

Answer 25

sin(a)cos(b) - cos(a)sin(b)

Question 26

sin(a)cos(b) - cos(a)sin(b)

Answer 26

sin(a-b)

Question 27

cos(a+b)

Answer 27

cos(a)cos(b) - sin(a)sin(b)

Question 28

cos(a)cos(b) - sin(a)sin(b)

Answer 28

cos(a+b)

Question 29

cos(a-b)

Answer 29

cos(a)cos(b) + sin(a)sin(b)

Question 30

cos(a)cos(b) + sin(a)sin(b)

Answer 30

cos(a-b)

Question 31

tg(a+b)

Answer 31

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

Question 32

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

Answer 32

tg(a+b)

Question 33

tg(a-b)

Answer 33

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

Question 34

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

Answer 34

tg(a-b)

Question 35

sin(a)sin(b)

Answer 35

(1/2) * ( cos(a-b) - cos(a+b) )

Question 36

(1/2) * ( cos(a-b) - cos(a+b) )

Answer 36

sin(a)sin(b)

Question 37

sin(a)cos(b)

Answer 37

(1/2) * ( sin(a-b) + sin(a+b) )

Question 38

(1/2) * ( sin(a-b) + sin(a+b) )

Answer 38

sin(a)cos(b)

Question 39

cos(a)cos(b)

Answer 39

(1/2) * ( cos(a-b) + cos(a+b) )

Question 40

(1/2) * ( cos(a-b) + cos(a+b) )

Answer 40

cos(a)cos(b)

Question 41

sin^2( a/2 )

Answer 41

( 1 - cos(a) ) / 2

Question 42

( 1 - cos(a) ) / 2

Answer 42

sin^2( a/2 )

Question 43

cos^2( a/2 )

Answer 43

( 1 + cos(a) ) / 2

Question 44

( 1 + cos(a) ) / 2

Answer 44

cos^2( a/2 )

Question 45

tg( a/2 )

Answer 45

sin(a) / ( 1 + cos(a) ) или ( 1 - cos(a) ) / sin(a)

Question 46

sin(a) / ( 1 + cos(a) )

Answer 46

tg( a/2 )

Question 47

( 1 - cos(a) ) / sin(a)

Answer 47

tg( a/2 )

Question 48

sin( 2a )

Answer 48

2*sin(a)cos(a)

Question 49

cos( 2a )

Answer 49

cos^2(a) - sin^2(a) или 2*cos^2(a) - 1 или 1 - 2*sin^2(a)

Question 50

cos^2(a) - sin^2(a)

Answer 50

cos( 2a )

Question 51

2*cos^2(a) - 1

Answer 51

cos( 2a )

Question 52

1 - 2*sin^2(a)

Answer 52

cos( 2a )

Question 53

tg( 2a )

Answer 53

2*tg(a) / ( 1-tg^2(a) )

Question 54

2*tg(a) / ( 1-tg^2(a) )

Answer 54

tg( 2a )

Question 55

sin(x) = 0

Answer 55

pi*k

Question 56

sin(x) = 1/2

Answer 56

pi/6 + 2*pi*k и 5*pi/6 + 2*pi*k (30, 150)

Question 57

sin(x) = -1/2

Answer 57

-pi/6 + 2*pi*k и -5*pi/6 + 2*pi*k (210, 330)

Question 58

sin(x) = sqr(2) / 2

Answer 58

pi/4 + 2*pi*k и 3*pi/4 + 2*pi*k (45, 135)

Question 59

sin(x) = - sqr(2) / 2

Answer 59

-pi/4 + 2*pi*k и -3*pi/4 + 2*pi*k (225, 315)

Question 60

sin(x) = sqr(3) / 2

Answer 60

pi/3 + 2*pi*k и 2*pi/3 + 2*pi*k (60, 120)

Question 61

sin(x) = - sqr(3) / 2

Answer 61

-pi/4 + 2*pi*k и -2*pi/3 + 2*pi*k (240, 300)

Question 62

sin(x) = 1

Answer 62

pi/2 + 2*pi*k (90)

Question 63

sin(x) = -1

Answer 63

-pi/2 + 2*pi*k (270)

Question 64

cos(x) = 0

Answer 64

pi/2 + pi*k (90, 270)

Question 65

cos(x) = 1/2

Answer 65

±pi/3 + 2*pi*k (60, 300)

Question 66

cos(x) = -1/2

Answer 66

±2*pi/3 + 2*pi*k (120, 240)

Question 67

cos(x) = sqr(2) / 2

Answer 67

±pi/4 + 2*pi*k (45, 315)

Question 68

cos(x) = - sqr(2) / 2

Answer 68

±3*pi/4 + 2*pi*k (135, 225)

Question 69

cos(x) = sqr(3) / 2

Answer 69

±pi/6 + 2*pi*k (30, 330)

Question 70

cos(x) = - sqr(3) / 2

Answer 70

±5*pi/6 + 2*pi*k (150, 210)

Question 71

cos(x) = 1

Answer 71

2*pi*k (0)

Question 72

cos(x) = -1

Answer 72

pi + 2*pi*k (180)

Question 73

tg(x) = 0

Answer 73

pi*k (0, 180)

Question 74

tg(x) = 1 / sqr(3)

Answer 74

pi/6 + 2*pi*k и 7*pi/6 + 2*pi*k (30, 210)

Question 75

tg(x) = 1

Answer 75

pi/4 + 2*pi*k и 5*pi/4 + 2*pi*k (45, 225)

Question 76

tg(x) = sqr(3)

Answer 76

pi/3 + 2*pi*k и 4*pi/3 + 2*pi*k (60, 240)