Question

Determine o período e as raizes das seguintes funções trigonométricas:

a) y = sen (2x+ pi/3)
b) y = cos (5x+7pi/6)
c) y = tan (-3x+pi/4)

Answer 1

a)  k = 2

Período

$\boxed{\mathsf{P = \frac{2\pi }{|k|} }}$

P = 2π/2

P = π

Raízes

Sen(2x +π/3) = 0

2x +π/3 = 0

2x = -π/3

x = -π/6

→ x , x + | π/k | , x + | 2π/k |

-π/6 +π/2

(-π +3π)/6

2π/6

π/3

π/3 +π/2

(+2π +3π)/6

5π/6

Sen(0) ; Sen(180) ; Sen(360)

-π/6 ; π/3 ; 5π/6

b) k = 5

Período

$\boxed{\mathsf{P = \frac{2\pi }{|k|} }}$

P = 2π/5

Raízes

Cos(5x +7π/6) = 0

5x = -7π/6

x = -7π/30

→ x + | π/2k | ; x + | 3π/2k |

-7π/30 + π/10

(-7π +3π)/30

-4π/30

-2π/15

-7π/30 + 3π/10

(-7π + 9π)/30

2π/30

π/15

-2π/15 ; π/15

c) k = -3

Período

$\boxed{\mathsf{P = \frac{\pi }{|k|} }}$

P = π/3

Raízes

Tan(-3x +π/4) = 0

π/4 = 3x

π/12 = x

→ x ; x + |4x|

π/12 +4π/12

5π/12

π/12 ; 5π/12