use the even - odd properties of the trigonometric functions to find the exact va\n\\( \\sin ( - 45 ^ {…
use the even - odd properties of the trigonometric functions to find the exact va\n\\( \\sin ( - 45 ^ { \\circ } ) \\)\nselect the correct choice below and fill in any answer boxes in your choice.\n\\( \\bigcirc \\) a. \\( \\sin ( - 45 ^ { \\circ } ) = \\)\n(simplify your answer, including any radicals. use integers or fractions\n\\( \\bigcirc \\) b. the answer is undefined.
Answer
Explanation:
Step1: Recall the odd - function property of sine
The sine function has the property ( \sin(-\theta)=-\sin\theta).
Step2: Substitute (\theta = 45^{\circ})
We know that ( \sin(45^{\circ})=\frac{\sqrt{2}}{2}). Using the odd - function property ( \sin(-45^{\circ})=-\sin(45^{\circ})). Substituting the value of ( \sin(45^{\circ})), we get ( \sin(-45^{\circ})=-\frac{\sqrt{2}}{2}).
Answer:
A. ( \sin(-45^{\circ})=-\frac{\sqrt{2}}{2})