Question

Which expression is equivalent to cos120°? ° cos240° cos300° cos420°?

Answer 1

Correct option is 1.

Step-by-step explanation:

We have to find the expression which is equivalent to cos 120°

Expression:
`\cos 120^\circ`

The given expression is equivalent to those whose value is same as
`\cos 120^\circ`

`\cos 120^\circ= \cos (180-60)`

`\cos 120^\circ= -\cos 60`

`\cos 120^\circ= -(1)/(2)`

value of cos 120° in second quadrant is negative.

Option 1 :
`\cos 240^(\circ)`

`\cos 240^(\circ)= \cos (180+60)= -\cos 60`

`\cos 240^(\circ)= -(1)/(2)`

Value is same i.e equivalent

Option 2 :
`\cos 300^(\circ)`

`\cos 300^\circ= \cos (360-60)`

`\cos 300^\circ= \cos (2* 180- 60)`

`\cos 300^\circ= \cos (60)`

`\cos 300^\circ= (1)/(2)`

Not equivalent

Option 3 :
`\cos 420^\circ`

`\cos 420^\circ= \cos (360+60)`

`\cos 300^\circ= \cos (2* 180+60)`

`\cos 420^\circ= \cos 60`

`\cos 420^\circ= (1)/(2)`

Not equivalent

∴ Correct option is 1.

`\cos 120^\circ=\cos 240^\circ=-(1)/(2)`

Answer 2

Option 1 - cos 240°

Explanation:

Given : Expression
`\cos 120^\circ`

To find : Which expression is equivalent to given expression ?

Solution :

The given expression is equivalent to those whose value is same as
`\cos 120^\circ`

Value of

`\cos 120^\circ= \cos (180-60)`

`\cos 120^\circ= -\cos 60`

`\cos 120^\circ= -(1)/(2)`

value of cos in second quadrant is negative.

Option 1 :
`\cos 240^\circ`

`\cos 240^\circ= \cos (180+60)`

`\cos 240^\circ= -\cos 60`

`\cos 240^\circ= -(1)/(2)`

Equivalent

Option 2 :
`\cos 300^\circ`

`\cos 300^\circ= \cos (360-60)`

`\cos 300^\circ= \cos (2* 180- 60)`

`\cos 300^\circ= \cos (60)`

`\cos 300^\circ= (1)/(2)`

Not equivalent

Option 3 :
`\cos 420^\circ`

`\cos 420^\circ= \cos (360+60)`

`\cos 300^\circ= \cos (2* 180+60)`

`\cos 420^\circ= \cos 60`

`\cos 420^\circ= (1)/(2)`

Not equivalent

Therefore, Correct option is 1.

`\cos 120^\circ=\cos 240^\circ=-(1)/(2)`