Question

Find cos O if sinO = sqrt2/2 is in the second quadrant

Answer 1

D.
`-(√(2) )/(2)`

Explanation:

So, on a regular coordinate plane, coordinates are written (x,y)

well, in trig, coordinates are written (cosθ, sinθ).

if sinθ=
`(√(2) )/(2)` in the second quadrant, then look for the "y-value" that says

if you don't have a unit circle to look at, then it helps to know that the fraction
`(√(2) )/(2)` is ONLY found with ITSELF OR THE NEGATIVE OF ITSELF. it is never paired with another number.

this means that this number will only be seen in the coordinates

`((√(2) )/(2) ,(√(2) )/(2))\\(-(√(2) )/(2),(√(2) )/(2))\\(-(√(2) )/(2),-(√(2) )/(2))\\((√(2) )/(2),-(√(2) )/(2))`

use this knowledge along with knowing the signs in each quadrant:

Q1: (+,+)

Q2: (–,+)

Q3: (–,–)

Q4: (+,–)