What is the value of cos 120 degree

Find the Value of cos 120 degree

What is the value of cos 120 degree ? The value of cos 120 degrees in terms of fraction is -1/2 or equal to minus half which can be written as (- ½ ) or the value of cos 120° in terms of decimal is (-0.5). We know that the value of cos 120° can be converted from degree to radian. To covert degree to radian we have to use this formula θ in radians = θ in degrees × (π/180°). Cos 120 degrees can be written as cos (120° × π/180°) or cos (2π/3) or cos (2.094395. . .) in terms of radians.

Value of trigonometric ratios for different angles

Find the value of cos 120 degree : There are some standard which are generally used in Trigonometric Functions Table 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. So we are going to make a single table for all trigonometric ratios Example – sin 0 degree, sin 30 degree, sin 45 degree, sin 60 degree, sin 90 degree. The trigonometric functions are namely sin theta function, cos theta function, tan theta function, cot theta function, sec theta function, and cosec theta function.

Trigonometry Ratio Table
Angles (In Degrees)	0	30	45	60	90	180	270	360
Angles (In Radians)	0	π/6	π/4	π/3	π/2	π	3π/2	2π
sin	0	1/2	1/√2	√3/2	1	0	−1	0
cos	1	√3/2	1/√2	1/2	0	−1	0	1
tan	0	1/√3	1	√3	Not Defined	0	Not Defined	0
cot	Not Defined	√3	1	1/√3	0	Not Defined	0	Not Defined
cosec	Not Defined	2	√2	2/√3	1	Not Defined	−1	Not Defined
sec	1	2/√3	√2	2	Not Defined	−1	Not Defined	1

How to find the value of Cos 120 degree

We have to split 120 degree in terms of two trigonometric angles 90° + 30° or 180° – 60°. Value of these 30°, 90° and 180° can be taken from trigonometry function sin theta cos theta table. What is the value of cos 120 degree ? We can represent 120 degree as 180° – 60° = 120° or 90° + 30° = 120°. We must know these two trigonometric functions cos(180° – x) = – cos x and cos (90° + x) = -sin x. Now we can find the value of cos 120 degree easily. Please follow below steps – Please follow this link of Explanation of Mathematics formula – Click

• As mentioned in the solution given below, 120° can be represented in terms of two angles i.e. either 90° or 180°.
• We can show that 120 degrees can be represented in two angles, whose value can be taken from trigonometry table.
• 90 degree and 180 degree
• 180° – 60° = 120° ———– (1)
• 90° + 30° = 120° ———— (2)
• Let’s use these now.
• Cos 120° = cos(180° – 60°) = – cos 60° = -½ (since cos(180° – x) = – cos x)
• Cos 120° = cos(90° + 30°) = – sin 30° = -½ (we know that cos (90° + x) = -sin x)

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