To find an equivalent sine ratio to sin 44°, we can use the fact that sine is a periodic function with a period of 360 degrees (or 2π radians). This means that if we add or subtract multiples of 360 degrees to an angle, the sine value remains the same.
Since 44° is less than 90°, we can find an equivalent sine ratio by subtracting multiples of 360 degrees from 44° to bring it within the first quadrant (0° to 90°) where the sine function is positive.
One way to do this is by subtracting 360° from 44° until we get an angle within the first quadrant. Let's calculate the equivalent sine ratio:
44° - 360° = -316° (outside the first quadrant)
-316° - 360° = -676° (outside the first quadrant)
-676° - 360° = -1036° (outside the first quadrant)
By subtracting multiples of 360°, we can see that the equivalent angle in the first quadrant is 44° - 3(360°) = 44° - 1080° = -1036°.
Now, we can use the symmetry property of the sine function to find the equivalent sine ratio:
sin(-1036°) = sin(180° - 1036°) = sin(-856°)
Therefore, an equivalent sine ratio to sin 44° is sin(-856°).