Respuesta :
Answer:
Option 1 - cos 240°
Step-by-step explanation:
Given : Expression [tex]\cos 120^\circ[/tex]
To find : Which expression is equivalent to given expression ?
Solution :
The given expression is equivalent to those whose value is same as [tex]\cos 120^\circ[/tex]
Value of
[tex]\cos 120^\circ= \cos (180-60)[/tex]
[tex]\cos 120^\circ= -\cos 60[/tex]
[tex]\cos 120^\circ= -\frac{1}{2}[/tex]
value of cos in second quadrant is negative.
Option 1 : [tex]\cos 240^\circ[/tex]
[tex]\cos 240^\circ= \cos (180+60)[/tex]
[tex]\cos 240^\circ= -\cos 60[/tex]
[tex]\cos 240^\circ= -\frac{1}{2}[/tex]
Equivalent
Option 2 : [tex]\cos 300^\circ[/tex]
[tex]\cos 300^\circ= \cos (360-60)[/tex]
[tex]\cos 300^\circ= \cos (2\times 180- 60)[/tex]
[tex]\cos 300^\circ= \cos (60)[/tex]
[tex]\cos 300^\circ= \frac{1}{2}[/tex]
Not equivalent
Option 3 : [tex]\cos 420^\circ[/tex]
[tex]\cos 420^\circ= \cos (360+60)[/tex]
[tex]\cos 300^\circ= \cos (2\times 180+60)[/tex]
[tex]\cos 420^\circ= \cos 60[/tex]
[tex]\cos 420^\circ= \frac{1}{2}[/tex]
Not equivalent
Therefore, Correct option is 1.
[tex]\cos 120^\circ=\cos 240^\circ=-\frac{1}{2}[/tex]
Answer:
Correct option is 1.
Step-by-step explanation:
We have to find the expression which is equivalent to cos 120°
Expression: [tex]\cos 120^\circ[/tex]
The given expression is equivalent to those whose value is same as [tex]\cos 120^\circ[/tex]
[tex]\cos 120^\circ= \cos (180-60)[/tex]
[tex]\cos 120^\circ= -\cos 60[/tex]
[tex]\cos 120^\circ= -\frac{1}{2}[/tex]
value of cos 120° in second quadrant is negative.
Option 1 : [tex]\cos 240^{\circ}[/tex]
[tex]\cos 240^{\circ}= \cos (180+60)= -\cos 60[/tex]
[tex]\cos 240^{\circ}= -\frac{1}{2}[/tex]
Value is same i.e equivalent
Option 2 : [tex]\cos 300^{\circ}[/tex]
[tex]\cos 300^\circ= \cos (360-60)[/tex]
[tex]\cos 300^\circ= \cos (2\times 180- 60)[/tex]
[tex]\cos 300^\circ= \cos (60)[/tex]
[tex]\cos 300^\circ= \frac{1}{2}[/tex]
Not equivalent
Option 3 : [tex]\cos 420^\circ[/tex]
[tex]\cos 420^\circ= \cos (360+60)[/tex]
[tex]\cos 300^\circ= \cos (2\times 180+60)[/tex]
[tex]\cos 420^\circ= \cos 60[/tex]
[tex]\cos 420^\circ= \frac{1}{2}[/tex]
Not equivalent
∴ Correct option is 1.
[tex]\cos 120^\circ=\cos 240^\circ=-\frac{1}{2}[/tex]
