Question

Pre-Cal - Someone please help! (Image Attached)

Answer 1

Note that
`\displaystyle{ \sin30^(\circ)= (1)/(2)` and
`\displaystyle{ \cos30^(\circ)= ( √(3))/(2)`.

From the unit circle, we can check that
`\sin30^(\circ)` and
`\sin(-30)^(\circ)` have the same value, but opposite signs, that is:


`\sin(-30)^(\circ)=-\sin(30)^(\circ)=-(1)/(2)`.


Thus,

`\displaystyle{ \cos(x-y)= \cos(-30^(\circ)-60^(\circ))=cos(-90^(\circ))`.


Note that
`cos(-90^(\circ))` is the x-coordinate of the lowest point on the unit circle, that is (0, -1). Thus
`cos(-90^(\circ))=0`


Answer: 0