write the expression as a function of θ, with no angle measure involved. sin(θ - 180°) sin(θ - 180°)=□…

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.)

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.)

Answer

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)