Question

What is the exact value of arcsin(−√2/2) ?

Answer 1

Answer:5Π/4

Step-by-step explanation:

arcsin(−√2/2) = -45°

Note that the angle is negative and according to quadrant, sine is negative at the 3rd and 4th quadrant.

In the 3rd quadrant, the equivalent angle is (180+theta) while at the 4th quadrant it is (360-theta.)

Using the 3rd quadrant which will give us the least value,

theta = 180+45

= 225° (note that the minus sign only tells us the quadrant sine falls into, hence we cant use the minus during addition)

therefore theta = 225°

Since 180° = Πrad

225° to rad = 225×Πrad/180

= 5Π/4 rad