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anonymous

  • 5 years ago

tan2θ−√3tanθ=0 Find all solutions in the interval [0,360°)

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  1. anonymous
    • 5 years ago
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    thanks for helping

  2. anonymous
    • 5 years ago
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    tan(2x) = 2tanx/(1- (tanx)^2) tan2x - sqrt(3)tanx = 2tanx/(1- (tanx)^2) - sqrt(3)tanx = 0 2tanx - (1- (tanx)^2)) *[ sqrt(3)tanx] = 0 2-1+ sqrt(3) (tanx)^2 = 0 now solve for tanx!

  3. anonymous
    • 5 years ago
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    so is it tanx=sqrt (1/1+sqrt3)??? then how do i convert it to intervals of [0,360degrees)?

  4. anonymous
    • 5 years ago
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    thanks for coming back!

  5. anonymous
    • 5 years ago
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    actually, it's tanx = sqrt(1/sqrt3)

  6. anonymous
    • 5 years ago
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    so... actually tanx is equal to plus or minus sqrt(1/sqrt3).. Positive right hand side: Take the inverse tangent to get 37.22 degrees... Now the only other value which equals sqrt(1/sqrt3) is 180 degrees plus that Negative right hand side: Take the inverse tangent to get 322.77 degress... The only other tan of a value to equal -sqrt(1/sqrt3) is 180 degrees less than that!

  7. anonymous
    • 5 years ago
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    so, is the solution set: 37, 143, 217 322) ????

  8. anonymous
    • 5 years ago
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    yup! Good job!

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