find all angles between 0 degrees 360 degree that satisfy the following trig ratios.
a) sintheta= -1 over sqaure root2
To find all angles between 0 degrees and 360 degrees that satisfy the trigonometric ratio sin(theta) = -1/sqrt(2), we can use the inverse sine function (also known as arcsin).
We know that sin(theta) = -1/sqrt(2), so we can write this as sin(theta) = -sqrt(2)/2.
The inverse sine function, arcsin, will give us the angle whose sine is a given value. In this case, we want to find the angle whose sine is -sqrt(2)/2.
Using a calculator with inverse sine function (sin^(-1) or arcsin), we can find that arcsin(-sqrt(2)/2) is -45 degrees.
Since -45 degrees is in the range of 0-360 degrees, one possible angle that satisfies the trigonometric ratio is -45 degrees.
To find the other possible angle, we can add 180 degrees to the first angle to account for the symmetry of the sine function.
-45 degrees + 180 degrees = 135 degrees
Therefore, the angles between 0 degrees and 360 degrees that satisfy sin(theta) = -1/sqrt(2) are -45 degrees and 135 degrees.