Cos 150 Degrees

The value of cos 150 degrees is -0.8660254. . .. Cos 150 degrees in radians is written as cos (150° × π/180°), i.e., cos (5π/6) or cos (2.617993. . .). In this article, we will discuss the methods to find the value of cos 150 degrees with examples.

• Cos 150°: -0.8660254. . .
• Cos 150° in fraction: −√3/2
• Cos (-150 degrees): -0.8660254. . .
• Cos 150° in radians: cos (5π/6) or cos (2.6179938 . . .)

What is the Value of Cos 150 Degrees?

The value of cos 150 degrees in decimal is -0.866025403. . .. Cos 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179 . . .
∴ cos 150° = cos(2.6179) = −√3/2 or -0.8660254. . .

Explanation:

For cos 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 150° value = −√3/2 or -0.8660254. . .
Since the cosine function is a periodic function, we can represent cos 150° as, cos 150 degrees = cos(150° + n × 360°), n ∈ Z.
⇒ cos 150° = cos 510° = cos 870°, and so on.
Note: Since, cosine is an even function, the value of cos(-150°) = cos(150°).

Methods to Find Value of Cos 150 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 150° is given as -0.86602. . .. We can find the value of cos 150 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 150° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 150 degrees as:

• ± √(1-sin²(150°))
• ± 1/√(1 + tan²(150°))
• ± cot 150°/√(1 + cot²(150°))
• ±√(cosec²(150°) - 1)/cosec 150°
• 1/sec 150°

Note: Since 150° lies in the 2nd Quadrant, the final value of cos 150° will be negative.

We can use trigonometric identities to represent cos 150° as,

• -cos(180° - 150°) = -cos 30°
• -cos(180° + 150°) = -cos 330°
• sin(90° + 150°) = sin 240°
• sin(90° - 150°) = sin(-60°)

Cos 150 Degrees Using Unit Circle

To find the value of cos 150 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis.
• The cos of 150 degrees equals the x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.

Hence the value of cos 150° = x = -0.866 (approx)

☛ Also Check:

• cos 60 degrees
• cos 53 degrees
• cos 120 degrees
• cos 69 degrees
• cos 720 degrees
• cos 24 degrees

FAQs on Cos 150 Degrees

What is Cos 150 Degrees?

Cos 150 degrees is the value of cosine trigonometric function for an angle equal to 150 degrees. The value of cos 150° is −√3/2 or -0.866 (approx)

What is the Value of Cos 150 Degrees in Terms of Tan 150°?

We know, using trig identities, we can write cos 150° as -1/√(1 + tan²(150°)). Here, the value of tan 150° is equal to -0.577350.

What is the Value of Cos 150° in Terms of Cosec 150°?

Since the cosine function can be represented using the cosecant function, we can write cos 150° as -[√(cosec²(150°) - 1)/cosec 150°]. The value of cosec 150° is equal to 2.

How to Find the Value of Cos 150 Degrees?

The value of cos 150 degrees can be calculated by constructing an angle of 150° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of cos 150° is equal to the x-coordinate (-0.866). ∴ cos 150° = -0.866.

How to Find Cos 150° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 150° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(150°))
• ± 1/√(1 + tan²(150°))
• ± cot 150°/√(1 + cot²(150°))
• ± √(cosec²(150°) - 1)/cosec 150°
• 1/sec 150°

☛ Also check: trigonometric table