Question

Help Please! (100 points!)

Answer 1

(cos90°) (cos30°) – (sin90°) (sin30°)

`cos (90°) = 0`

`sin (90°) = 1`

`sin (30°) =(1)/(2)`

`cos (30°) = ( √(3) )/(2)`

Simplified :

`(cos90) (cos30) – (sin90) (sin30) = - (1)/(2)`

So, B)
`cos (120°) = - (1)/(2)`

Answer 2

B is only true and the correct option.

Step-by-step explanation:

`\left(cos90\right)\left(cos30\right)-\left(sin90\right)\left(sin30\right)`

• 
  `\quad \cos \left(90^(\circ \:)\right)=0`

• 
  `\quad \sin \left(90^(\circ \:)\right)=1`

• 
  `\quad \sin \left(30^(\circ \:)\right)=(1)/(2)`

• 
  `\cos \left(30^(\circ \:)\right)=(√(3))/(2)`

when simplified:

`\left(cos90\right)\left(cos30\right)-\left(sin90\right)\left(sin30\right) = \ -(1)/(2)`

from options:

A)
`cos60^\circ =(1)/(2)`

✔B)
`\cos \left(120^(\circ \:)\right) = -(1)/(2)`

C)
`sin60^\circ = (√(3) )/(2)`

D)
`sin120^\circ = (√(3) )/(2)`