1. Use each trig ratio to determine all values of theta, to the nearest degree for
0<=theta<=360.
d)csc=sqaureroot2 (no calc)
To solve for theta using csc(theta) = sqrt(2), we first find the value of sin(theta), since csc(theta) is the reciprocal of sin(theta).
Reciprocal of csc(theta) = sin(theta)
Therefore, sin(theta) = 1/csc(theta) = 1/(sqrt(2))
To find the values of theta, we can check for the angles where sin(theta) = 1/(sqrt(2)).
Using the unit circle, we know that sin(theta) = 1/(sqrt(2)) at the angles 45 degrees and 225 degrees. However, this is only true for the principal angle. Since the range of theta is 0 to 360 degrees, we need to find all angles that have a sin(theta) = 1/(sqrt(2)) by adding or subtracting multiples of 360 degrees.
Therefore, the values of theta to the nearest degree for sin(theta) = 1/(sqrt(2)) are:
45 degrees, 225 degrees, 405 degrees (45 + 360), 585 degrees (225 + 360).
So, theta = 45 degrees, 225 degrees, 405 degrees, 585 degrees.