Question

write the expression as a function of θ, with no angle measure involved. sin(θ - 180°) sin(θ - 180°)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Use the sine difference formula

The formula for \(\sin(A - B)=\sin A\cos B-\cos A\sin B\). Here \(A = \theta\) and \(B=180^{\circ}\). So \(\sin(\theta - 180^{\circ})=\sin\theta\cos180^{\circ}-\cos\theta\sin180^{\circ}\).

Step2: Substitute the values of trigonometric functions

We know that \(\cos180^{\circ}=- 1\) and \(\sin180^{\circ}=0\). Substituting these values into the above - expression: \(\sin\theta\times(-1)-\cos\theta\times0\).

Step3: Simplify the expression

\(\sin\theta\times(-1)-\cos\theta\times0=-\sin\theta - 0\).

Answer:

\(-\sin\theta\)