Use the rated acute angle to state an equivalent expression
sin 350
-sin10°
To find an equivalent expression for sin 350 using the rated acute angle, we first need to find an angle between 0 and 90 degrees that has the same sine value. Since 350 degrees is greater than 360 degrees, we can subtract 360 from it repeatedly until we get a value between 0 and 360.
350 - 360 = -10
Since -10 is negative, we still need to subtract 360 again:
-10 - 360 = -370
Now we have an angle, -370 degrees, that is equivalent to 350 degrees. However, we need to find the equivalent expression in terms of a positive acute angle. To do this, we add 360 degrees to -370 degrees:
-370 + 360 = -10
Now we have an angle, -10 degrees, that is equivalent to 350 degrees. But we want the equivalent expression in terms of a positive acute angle. Since sin is positive in the second and fourth quadrants, both of which are acute angles, we can find the reference angle in the first quadrant by subtracting -10 degrees from 180 degrees.
180 - (-10) = 190 degrees
Therefore, the equivalent expression for sin 350 in terms of a positive acute angle is sin 190 degrees.