Как найти косинус 5пи на 3

The value of cos 5pi/3 is 0.5. Cos 5pi/3 radians in degrees is written as cos ((5π/3) × 180°/π), i.e., cos (300°). In this article, we will discuss the methods to find the value of cos 5pi/3 with examples.

• Cos 5pi/3: 1/2
• Cos 5pi/3 in decimal: 0.5
• Cos (-5pi/3): 0.5 or 1/2
• Cos 5pi/3 in degrees: cos (300°)

What is the Value of Cos 5pi/3?

The value of cos 5pi/3 in decimal is 0.5. Cos 5pi/3 can also be expressed using the equivalent of the given angle (5pi/3) in degrees (300°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/3 radians = 5pi/3 × (180°/pi) = 300° or 300 degrees
∴ cos 5pi/3 = cos 5π/3 = cos(300°) = 1/2 or 0.5

Explanation:

For cos 5pi/3, the angle 5pi/3 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 5pi/3 value = 1/2 or 0.5
Since the cosine function is a periodic function, we can represent cos 5pi/3 as, cos 5pi/3 = cos(5pi/3 + n × 2pi), n ∈ Z.
⇒ cos 5pi/3 = cos 11pi/3 = cos 17pi/3 , and so on.
Note: Since, cosine is an even function, the value of cos(-5pi/3) = cos(5pi/3).

Methods to Find Value of Cos 5pi/3

The cosine function is positive in the 4th quadrant. The value of cos 5pi/3 is given as 0.5. We can find the value of cos 5pi/3 by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 5pi/3 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 5pi/3 as:

• ± √(1-sin²(5pi/3))
• ± 1/√(1 + tan²(5pi/3))
• ± cot(5pi/3)/√(1 + cot²(5pi/3))
• ±√(cosec²(5pi/3) – 1)/cosec(5pi/3)
• 1/sec(5pi/3)

Note: Since 5pi/3 lies in the 4th Quadrant, the final value of cos 5pi/3 will be positive.

We can use trigonometric identities to represent cos 5pi/3 as,

• -cos(pi – 5pi/3) = -cos(-2pi/3)
• -cos(pi + 5pi/3) = -cos 8pi/3
• sin(pi/2 + 5pi/3) = sin 13pi/6
• sin(pi/2 – 5pi/3) = sin(-7pi/6)

Cos 5pi/3 Using Unit Circle

To find the value of cos 5π/3 using the unit circle:

• Rotate ‘r’ anticlockwise to form 5pi/3 angle with the positive x-axis.
• The cos of 5pi/3 equals the x-coordinate(0.5) of the point of intersection (0.5, -0.866) of unit circle and r.

Hence the value of cos 5pi/3 = x = 0.5

☛ Also Check:

• sin 5pi/12
• tan 5pi/4
• sin 3pi/2
• tan 2pi
• sec pi/3
• tan pi/6

FAQs on Cos 5pi/3

What is Cos 5pi/3?

Cos 5pi/3 is the value of cosine trigonometric function for an angle equal to 5π/3 radians. The value of cos 5pi/3 is 1/2 or 0.5

How to Find Cos 5pi/3 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 5pi/3 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(5pi/3))
• ± 1/√(1 + tan²(5pi/3))
• ± cot(5pi/3)/√(1 + cot²(5pi/3))
• ±√(cosec²(5pi/3) – 1)/cosec(5pi/3)
• 1/sec(5pi/3)

☛ Also check: trigonometric table

What is the Value of Cos 5pi/3 in Terms of Sec 5pi/3?

Since the secant function is the reciprocal of the cosine function, we can write cos 5pi/3 as 1/sec(5pi/3). The value of sec 5pi/3 is equal to 2.

What is the Value of Cos 5pi/3 in Terms of Cot 5pi/3?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 5pi/3 can be written as -cot(5pi/3)/√(1 + cot²(5pi/3)). Here, the value of cot 5pi/3 is equal to -0.57735.

How to Find the Value of Cos 5pi/3?

The value of cos 5pi/3 can be calculated by constructing an angle of 5π/3 radians with the x-axis, and then finding the coordinates of the corresponding point (0.5, -0.866) on the unit circle. The value of cos 5pi/3 is equal to the x-coordinate (0.5). ∴ cos 5pi/3 = 0.5.