Question

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

Answer 1

Answer:

Option 1 - cos 240°

Step-by-step 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

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

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

$\cos 120^\circ= -\frac{1}{2}$

value of cos in second quadrant is negative.

Option 1 : $\cos 240^\circ$

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

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

$\cos 240^\circ= -\frac{1}{2}$

Equivalent

Option 2 : $\cos 300^\circ$

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

$\cos 300^\circ= \cos (2\times 180- 60)$

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

$\cos 300^\circ= \frac{1}{2}$

Not equivalent

Option 3 : $\cos 420^\circ$

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

$\cos 300^\circ= \cos (2\times 180+60)$

$\cos 420^\circ= \cos 60$

$\cos 420^\circ= \frac{1}{2}$

Not equivalent

Therefore, Correct option is 1.

$\cos 120^\circ=\cos 240^\circ=-\frac{1}{2}$

Answer 2

Answer:

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 $\cos 120^\circ$

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

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

$\cos 120^\circ= -\frac{1}{2}$

value of cos 120° in second quadrant is negative.

Option 1 : $\cos 240^{\circ}$

$\cos 240^{\circ}= \cos (180+60)= -\cos 60$

$\cos 240^{\circ}= -\frac{1}{2}$

Value is same i.e equivalent

Option 2 : $\cos 300^{\circ}$

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

$\cos 300^\circ= \cos (2\times 180- 60)$

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

$\cos 300^\circ= \frac{1}{2}$

Not equivalent

Option 3 : $\cos 420^\circ$

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

$\cos 300^\circ= \cos (2\times 180+60)$

$\cos 420^\circ= \cos 60$

$\cos 420^\circ= \frac{1}{2}$

Not equivalent

∴ Correct option is 1.

$\cos 120^\circ=\cos 240^\circ=-\frac{1}{2}$