contestada

find all solutions of cosx-\sqrt(1-3cos^(2)x)=0 a. 60° + n360°, 300° + n360° b. 30° + n360°, 210° + n360° c. 30° + n360°, 330° + n360° d. 60° + n360°, 120° + n360°

Respuesta :

tomson1975

Greetings from Brasil...

The equation is:

COS X - √(1 - 3.COS² X) = 0

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

Otras preguntas