Question

find the exact value using a sum or difference identity. sin 390° hint: sin(a ± b) = sin a cos b ± cos a sin b cos(a ± b) = cos a cos b ∓ sin a sin b

Explanation:

Step1: Rewrite the angle

We know that \(390^{\circ}=360^{\circ} + 30^{\circ}\). So, \(\sin390^{\circ}=\sin(360^{\circ}+ 30^{\circ})\).

Step2: Apply the sum identity

Using the sum identity \(\sin(A + B)=\sin A\cos B+\cos A\sin B\), where \(A = 360^{\circ}\) and \(B=30^{\circ}\).
We know that \(\sin360^{\circ}=0\) and \(\cos360^{\circ}=1\).

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Step3: Calculate the value

Since \(\sin30^{\circ}=\frac{1}{2}\), the value of \(\sin(360^{\circ}+30^{\circ})\) is \(\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)