Solve for x
sec^2πx = 4/π
I don't understand this please help thanks!
sec^2πx = 4/π
I don't understand this please help thanks!
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sec²(πx) = 4/π
Substitute 1/cos²(πx) for sec²(πx):
1/cos²(πx) = 4/π
Multiply both sides by cos²(πx):
1 = {4/π}{cos²(πx)}
Multiply both sides by π/4:
cos²(πx)= π/4
Take the square root of both sides:
cos(πx) = ±sqrt(π/4)
Take the inverse cosine of both sides:
πx = cos^-1(±sqrt(π/4))
x = {1/π}cos^-1(±sqrt(π/4))
This is two answers:
x = {1/π}cos^-1(sqrt(π/4))
x = {1/π}cos^-1(-sqrt(π/4))
Now you need a calculator.
Substitute 1/cos²(πx) for sec²(πx):
1/cos²(πx) = 4/π
Multiply both sides by cos²(πx):
1 = {4/π}{cos²(πx)}
Multiply both sides by π/4:
cos²(πx)= π/4
Take the square root of both sides:
cos(πx) = ±sqrt(π/4)
Take the inverse cosine of both sides:
πx = cos^-1(±sqrt(π/4))
x = {1/π}cos^-1(±sqrt(π/4))
This is two answers:
x = {1/π}cos^-1(sqrt(π/4))
x = {1/π}cos^-1(-sqrt(π/4))
Now you need a calculator.