Question

deltamath
math| 4.3 day 2 and 3
given the following unit circle, rotate green dot to the appropriate angle and then find the exact
value of the function.
\\( \sin \left( - 45 ^ { \circ } \
ight) \\)
answer attempt 1 out of 2
\\( \sin \left( - 45 ^ { \circ } \
ight) = \\)
submit answer

Explanation:

Step1: Use the property of sine function

The sine function is an odd function, so $\sin(-\alpha)=-\sin\alpha$.
For $\sin(-45^{\circ})$, we have $\sin(-45^{\circ}) = -\sin(45^{\circ})$.

Step2: Recall the value of $\sin(45^{\circ})$

We know that $\sin(45^{\circ})=\frac{\sqrt{2}}{2}$.
Substituting this value into the equation from Step 1, we get $\sin(-45^{\circ})=-\frac{\sqrt{2}}{2}$.

Answer:

$-\frac{\sqrt{2}}{2}$