Chapter1 (Q3) Use the identities for the cosine of a sum or difference to write each expression as a function:a. \(Cos(0°+θ)\)b. \(Cos(90°+θ)\)c. \(Cos(180°+θ) \)d. \(Cos(270°+θ) \)
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Solution
a. \(Cos(0°+θ)=Cos0°cosθ-Sin0°sinθ←1×cosθ-0×sinθ \)=
b. \(Cos(90°+θ)=Cos90°cosθ-Sin90°sinθ←0×cosθ-1×sinθ \)=
c. \(Cos(180°+θ)=Cos180°cosθ-Sin180°sinθ←-1×cosθ-0×sinθ \)=
d. \(Cos(270°+θ)=Cos270°cosθ-Sin270°sinθ←0×cosθ-(-1)×sinθ \)=
Solution:
a. \(Cos(0°+θ)=Cos0°cosθ-Sin0°sinθ 1×cosθ-0×sinθ=cosθ \)
b. \( Cos(90°+θ)=Cos90°cosθ-Sin90°sinθ 0×cosθ-1×sinθ=sinθ \)
c. \( Cos(180°+θ)=Cos180°cosθ-Sin180°sinθ -1×cosθ-0×sinθ=-cosθ.\)
d. /(Cos(270°+θ)=Cos270°cosθ-Sin270°sinθ←0×cosθ-(-1