How do you verify cos 180° = -1?

Value of Cos 180 Degree (π) is -1

Proof

We can prove the Value of Cos 180 Degree (π) is -1 using cartesian plane and also mathematically.

Cartesian plane

Consider the unit circle in which the Cartesian plane is divided into four quadrants. To find the value of cos 180 degrees from the Cartesian plane, the value 180 degree takes place in the second quadrant. As the cosine values in the second quadrant always take a negative value.

From the value of cos 0, we will obtain the value of cos 180°.

We know that the exact value of cos 0 degrees is 1

So, cos 180 degree is -(cos 0) which is equal to -(1)

Therefore, the value of cos 180 degrees = -1

Mathematically

We know that,

180° – 0° = 180° ———– (1)

270° – 90° = 180° ———— (2)

So using equation (1)

The value of cos pi =Cos 180°

= cos(180° – 0°)

= – cos 0°

= – (1)

= – 1

Hence, the value of cos pi = -1

Alternative method

Using equation (2)

Cos 180°= cos(270° – 90°)

Cos 180°= – sin 90° (We know that cos ( 270° – a ) = – sin a)

The value of sin 90 degree is 1.

Substitute the value in the above relation, we get

Cos 180°= – (1) = -1

Therefore, the value of cos 180° is -1.

Cos 180°= -1

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