Solve the eq in the given interval: cos(60-x)= -0.4 -180<x<180

I get 60-x= 113.58 so x= - 53.58

And 60-x = 246.42 which doesnt belong to the domain, so I changed it to -113.58, so

X = - 173.58 but the answer in the book says 173.58. Is there a mistake in the book? Or Am I wrong?

I get 60-x= 113.58 so x= - 53.58

And 60-x = 246.42 which doesnt belong to the domain, so I changed it to -113.58, so

X = - 173.58 but the answer in the book says 173.58. Is there a mistake in the book? Or Am I wrong?

(edited 6 months ago)

Original post by olygilly

Solve the eq in the given interval: cos(60-x)= -0.4 -180<x<180

I get 60-x= 113.58 so x= - 53.58

And 60-x = 246.42 which does belong to the domain, so I changed it to -113.58, so

X = - 173.58 but the answer in the book says 173.58. Is there a mistake in the book? Or Am I wrong?

I get 60-x= 113.58 so x= - 53.58

And 60-x = 246.42 which does belong to the domain, so I changed it to -113.58, so

X = - 173.58 but the answer in the book says 173.58. Is there a mistake in the book? Or Am I wrong?

Book is correct and your woking is correct until you write x=- ... Is it (X = - 173.58) a typo?

(edited 6 months ago)

Yeah, just looks like a typo in the last line.

cos(60 - x) = -0.4

{-180 < x < 180}

For 60 - x:

=> 60 - (-180) = 240

=> 60 - 180 = -120

{-120 < 60 - x < 240}

60 - x = arccos(-0.4) = 113.58, -113.58,~~246.42~~

For 60 - x = 113.58:

=> x = 60 - 113.58 = -53.58

For 60 - x = -113.58:

=> x = 60 + 113.58 = 173.58

cos(60 - x) = -0.4

{-180 < x < 180}

For 60 - x:

=> 60 - (-180) = 240

=> 60 - 180 = -120

{-120 < 60 - x < 240}

60 - x = arccos(-0.4) = 113.58, -113.58,

For 60 - x = 113.58:

=> x = 60 - 113.58 = -53.58

For 60 - x = -113.58:

=> x = 60 + 113.58 = 173.58

(edited 5 months ago)

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