Where are the x-intercepts for f(x) = 4 cos(2x - π) from x = 0 to x = 2π?
Solution:
Given: x-intercepts for f(x) = 4 cos(2x - π) from x = 0 to x = 2π
We have to find if f(x) = 0
Consider x = π/4
f(π/4) = 4 cos(2π/4 - π)
Taking the LCM
f(π/4) = 4 cos[(2π - 4π)/4]
f(π/4) = 4 cos (-2π)/4
f(π/4) = 4 cos (-π)/2
f(π/4) = 4(0)
f(π/4) = 0
Consider x = 3π/4
f(3π/4) = 4 cos(2 × 3π/4 - π) = 4 cos[3π/2 - π]
Taking the LCM
f(3π/4) = 4 cos[3π - 2π]/2
f(3π/4) = 4 cos π/2
f(3π/4) = 4(0)
f(3π/4) = 0
Consider x = 5π/4
f(5π/4) = 4 cos(2 × 5π/4 - π) = 4 cos[5π/2 - π]
Taking the LCM
f(5π/4) = 4 cos[(5π - 2π)/2]
f(5π/4) = 4 cos (3π)/2
f(5π/4) = 4(0)
f(5π/4) = 0
Consider x = 7π/4
f(7π/4) = 4 cos(2 × 7π/4 - π)
= 4 cos[7π/2 - π]
Taking the LCM
f(7π/4) = 4 cos[(7π - 2π)/2]
f(7π/4) = 4 cos (5π)/2
f(7π/4) = 4(0)
f(7π/4) = 0
Therefore, the x-intercepts are π/4, 3π/4, 5π/4 and 7π/4.
Where are the x-intercepts for f(x) = 4 cos(2x - π) from x = 0 to x = 2π?
Summary:
The x-intercepts for f(x) = 4 cos(2x - π) from x = 0 to x = 2π are π/4, 3π/4, 5π/4 and 7π/4.
visual curriculum