- #1
metalscot
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The question is: Using Eulers formula for e^±iθ , obtain the trigometric identities for cos(θ1, θ2) and sin(θ1, θ2)
I think I have completed the real and imaginary solutions for the base e^+iθ using the real part cos(θ1+θ2)and imaginary isin(θ1+θ2)
Gaining
cos(θ1 + θ2) = cosθ1 cosθ2 - sinθ1 sinθ2
sin(θ1 + θ2) = sinθ1 cosθ2 + cosθ1 sinθ2
My problem is how to proceed from here for the base e^-iθ
should my real and imaginary parts be in the form
cos(θ1-θ2) + isin(θ1-θ2)
or
cos(θ1+θ2) - isin(θ1+θ2)
Thanks in advance for any help
I think I have completed the real and imaginary solutions for the base e^+iθ using the real part cos(θ1+θ2)and imaginary isin(θ1+θ2)
Gaining
cos(θ1 + θ2) = cosθ1 cosθ2 - sinθ1 sinθ2
sin(θ1 + θ2) = sinθ1 cosθ2 + cosθ1 sinθ2
My problem is how to proceed from here for the base e^-iθ
should my real and imaginary parts be in the form
cos(θ1-θ2) + isin(θ1-θ2)
or
cos(θ1+θ2) - isin(θ1+θ2)
Thanks in advance for any help