Provide the values of β that are the solutions to the equation:
2cos(3β+3π)=−2.
Solution:
2cos(3β+3π)=−2.
⎣⎡3β+3π=cos−1(−22)+2πk,k∈Z,3β+3π=−cos−1(−22)+2πk,k∈Z.
⎣⎡3β+3π=43π+2πk,k∈Z,3β+3π=−43π+2πk,k∈Z.
⎣⎡3β=125π+2πk,k∈Z,3β=−1213π+2πk,k∈Z.
⎣⎡β=365π+32πk,k∈Z,β=−3613π+32πk,k∈Z.
Answer:
β∈{365π+32πk}∪{−3613π+32πk},k∈Z
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