Question

Select all angle measures for which sin0= -√2/2

Answer 1

Option 1

Explanation:

`Total \: value \: of \: \pi \: in \: terms \: of \: angles \: = 180`

`So \: putting \: the \: of \: \pi \: in \: (3\pi)/(4) gives`

`(3 * 180)/(4) = 3 * 45 = 135 \: degrees`

`\sin(135) = (- √(2) )/(2) = (-1)/( √(2) )`

Answer 2

5π/4 & 7π/4 & 13π/4

Explanation:

For this problem, we simply need to find the value of theta for which arcsin(-sqrt(2)/2) is true. This value is π/4 or 45 degrees if we had a positive. To make the negative true, we need the angle to be in the third or fourth quadrants (i.e., 5π/4 and 7π/4). These are two of the answer choices. And then anytime these return (i.e., by adding 8/4 to either of these) should also be selected as a correct angle. Thus we get 13π/4 as the final angle.