Cos 120 Degree: Value and Other Details

Cos 120° is commonly used in both trigonometry and calculus in the higher grades. The relationship between different sides and angles of a triangle is referred to as trigonometry. Trigonometry is used in a range of tasks like engineering, aviation industry, construction of buildings, etc… Sine, cosine and tangent are the three major trigonometrical ratios that are used for the purpose of calculating trigonometrical sums. Cos is one of the 6 trigonometric functions and is widely used in both Mathematics and Physics.

The overall concept of trigonometry is based on a right-angled triangle. The value of cos 120° is -1/2 or -0.5 as it lies in the 2nd quadrant where cosine is negative. The formula of cosine is, cos x = (adjacent side) / (hypotenuse). Here, the adjacent side is adjacent to angle x, and the hypotenuse is the triangle’s longest side. Students can find the detailed explanation below.

Cos 120°: Value

In order to find the value of cos 120°, students need to draw a right-angled triangle (refer to the image below) and can use either of the two formulas i.e,
cos (180° – θ) = – cosθ
or
cos (90° + θ) = – sinθ.

Students must already know that cos θ = \(\frac{base}{hypotenuse}\) = \(\frac{b}{h}\)

It is important for the students to be able to identify the perpendicular, hypotenuse and base of the triangle. In the examination the values of a, b, h will be mentioned and based on these you can calculate cos θ.

Since we are already aware of the values of trigonometric angles for sin, cos and tan from 0 to 90. We will use the formula to find the value of cos 120.

Degrees	0°	30°	45°	60°	90°
sin	0	1/2	1/√2	√3/2	1
cos	1	√3/2	1/√2	1/2	0
tan	0	1/√3	1	√3	∞

Using cos (180° – θ) = – cosθ
1. cos 120° = cos (180° – 60°) = -cos 60 = -1/2.

Using cos (90° + θ) = – sinθ
1. cos (90° + 30°) = – sin30° = -1/2.

Trigonometrical Table: Cos 120

Now that you know the value of cosine 120°, let us provide you with the complete trigonometrical table:

Angles	0°	30° or π/6	45° or π/4	60° or π/3	90° or π/2	120° or 2π/3	180° or π	270° or 3π/2	360° or 2π
Sin	0	1/2	1/√2	√3/2	1	√3/2	0	−1	0
Cos	1	√3/2	1/√2	1/2	0	-1/2	−1	0	1
Tan	0	1/√3	1	√3	Not Defined	-√3	0	Not Defined	0
Cot	Not Defined	√3	1	1/√3	0	-1/√3	Not Defined	0	Not Defined
Cosec	Not Defined	2	√2	2/√3	1	2/√3	Not Defined	−1	Not Defined
Sec	1	2/√3	√2	2	Not Defined	-2	−1	Not Defined	1

Learn from Embibe

Students can access the following study materials for only on Embibe for their exam preparation:

NCERT Solutions	NCERT Books
Class 8 Mock Test Series	Class 8 Practice Questions
Class 9 Mock Test Series	Class 9 Practice Questions
Class 10 Mock Test Series	Class 10 Practice Questions
JEE Main Mock Tests (Class 11-12 PCM)	JEE Main Practice Questions (Class 11-12 PCM)
NEET Mock Tests (Class 11-12 PCB)	NEET Practice Questions (Class 11-12 PCB)

Trigonometrical Identities

Here are some identities based on which questions are asked:

a) sin (90° – A) = cos A
b) cos (90° – A) = sin A
c) tan (90° – A) = cot A
d) cot (90° – A) = tan A
e) sec (90° – A) = cosec A
f) cosec (90° – A) = sec A

Sample Questions

i) Evaluate cos 48° – sin 42°.
ii) Find cosec 31° – sec 59°.
iii) Solve cos 38° cos 52° – sin 38° sin 52° = 0.
iv) Evaluate sin 60° cos 30° + sin 30° cos 60°.
v) 2 tan² 45° + cos²30° – sin² 60°.
vi) Express the ratios cos A, tan A and sec A in terms of sin A.

FAQs

Frequently asked questions related to cos 120 degree is listed as follows:

Q.1. How do you find cos 120 without a calculator?
Ans. You can use both the following formulas
i) cos (180° – θ) = – cosθ
or
ii) cos (90° + θ) = – sinθ

Q.2. What is cos 120 in radians?
Ans. In radian, the value of cos 120 is 2π/3 i.e equal to -1/2.

Q.3. How do you evaluate cos 120?
Ans. The method to evaluate cosine 120 has been provided on this page.

Q.4. What is the value of cos 150 degrees?
Ans. Cos 15 equals -√3/2.

Q.5. What is the value of Cos 90?
Ans. The value of Cos 90 is 0.

So that is all the information on cos 120 and we have reached the end of our article. We hope the information was helpful. However, if you have further questions feel to use the comments section.