Hannah Kertzmann
Jan 05, 2025
what is the solution set to cos2x=0?
What is the solution set for the equation cos(2x) = 0? Thank you for your assistance!
2 Answers
Dec 14, 2024
Cos(2x) = 2cos²(x) -1 So substituting this we get
2cos² (x) – 1 =0
Now solve as a regular equation, add 1, divide by 2, take the square root
2cos² (x)= 1
cos²(x)=1/2
cos(x)= +/- √2/2
So at what angle does cosine (x-value) equal -√2/2 and positive √2/2?
45 degrees, 135, 225, 315 or use the ratio (180/pi) to convert to radian pi/4, 3pi/4, 5pi/4, 7pi/4
Alternatively, you could have replaced 2x with Θ to get
cos(Θ)=0
Think where does theta equal 0, that would be at Θ=pi/2 + 2(pi)(k) and Θ=3pi/2 + 2(pi)(k) where k is a positive integer
Next replace Θ with 2x
2x=pi/2 + 2(pi)k
Solve for x to get
x=pi/4 + pi(k)
x=3pi/4 + pi(k)
Then just plug in for k
When k=0, x= pi/4, 3pi/4
k=1 x = 5pi/4, 7pi/4 and so on
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