Please Help me with this trig function!!!! PLEASE PLEASE!!!?

Question

4 cos (2x + pi/4) = 2

Answer 1

If you're looking for just one value:

4 cos (2x + pi/4) = 2
cos(2x + pi/4) = 2/4 = 1/2
2x + pi/4 = cos^-1(1/2)
2x + pi/4 = pi/3
2x = pi/3 - pi/4 = pi/12
x = pi/24

If you're looking for all possible values:

4 cos (2x + pi/4) = 2
cos(2x + pi/4) = 2/4 = 1/2
2x + pi/4 = cos^-1(1/2)
2x + pi/4 = { pi/3 + k*2pi, -pi/3 + k*2pi }
2x = { pi/12 + k*2pi, -7pi/12 + k*2pi }
x = { pi/24 + k*pi, -7pi/24 + k*pi }
... where k is any integer.

Answer 2

you want to solve the equation?

I think so.

1) cos(2x+pi/4)=1/2 and cosy = 1/2 => y = pi/3

2) 2x + pi/4 = pi/3 + 2kp or 2x + pi/4 = -pi/3 + 2kpi

2x = pi/12 + 2kpi or 2x = -7pi/12 + 2kpi

3) x = pi/24 + kpi or x = -7pi/24 + kp

Answer 3

4 cos (2x + pi/4) = 2

cos (2x + pi/4) = 2/4

2x + pi/4 = cos^-1 2/4

2x = (cos^-1 2/4) - pi/4

x = ((cos^-1 2/4) - pi/4)/2

x = 29.607

Answer 4

4 cos (2x + pi/4) = 2

This isn't as tough as it looks.

Multiply both sides by 1/4
cos(2x + π/4) = 1/2
It turns out that the cos(π/3)=1/2

How do I know that? Because I've memorized the sine and cosine functions for 0, π/6, π/4, π/3, and π/2. It's REALLY simple
θ . . . . . . sin(θ) . . . . cos(θ
0 . . . . . .√(0/4) . . . . √(4/4)
π/6. . . . .√(1/4) . . . . √(3/4)
π/4. . . . .√(2/4) . . . . √(2/4)
π/3. . . . .√(3/4) . . . . √(1/4)
π/2. . . . .√(4/4) . . . . √(0/4)

So 2x+π/4 = π/3
Multiply both sides by 12
24x +3π = 4π
Add -3π to both sides...
24x = π
x = π/24

If your teacher likes to see angles in the other quadrants as well...
Since cos(θ) = cos(-θ)
2x+π/4 could also = -π/3
24x + 3π = -4π
24x = -7π
x = -7π/24

If your teacher likes to see the multiples of 2π built into your answers,
2x+π/4 = π/3 + 2nπ
24x + 3π = 4π + 24nπ
24x = π + 24nπ
x = π/24 + nπ where n is any integer.
AND
2x+π/4 = -π/3 + 2nπ
24x + 3π = -4π + 24nπ
24x = -7π + 24nπ
x = -7π/24 + nπ where n is any integer

You know what kind of answers your instructor wants.

Answer 5

4cos(2x + pi/4) = 2
cos(2x + pi/4) = 1/2

Either:

2x + pi/4 = 2n pi + pi / 3
x = (1/2) ( 2n pi + pi / 3 - pi / 4 )
x = (1/2) (2n pi + pi / 12)
x = n pi + pi / 24

or

2x + pi/4 = 2n pi - pi / 3
x = (1/2)( 2n pi - pi / 3 - pi / 4 )
x = (1/2)( 2n pi - 7pi / 12 )
x = n pi - 7pi / 24.