Cos 345 Degrees

The value of cos 345 degrees is 0.9659258. . .. Cos 345 degrees in radians is written as cos (345° × π/180°), i.e., cos (23π/12) or cos (6.021385. . .). In this article, we will discuss the methods to find the value of cos 345 degrees with examples.

• Cos 345°: 0.9659258. . .
• Cos 345° in fraction: (√6 + √2)/4
• Cos (-345 degrees): 0.9659258. . .
• Cos 345° in radians: cos (23π/12) or cos (6.0213859 . . .)

What is the Value of Cos 345 Degrees?

The value of cos 345 degrees in decimal is 0.965925826. . .. Cos 345 degrees can also be expressed using the equivalent of the given angle (345 degrees) in radians (6.02138 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 345 degrees = 345° × (π/180°) rad = 23π/12 or 6.0213 . . .
∴ cos 345° = cos(6.0213) = (√6 + √2)/4 or 0.9659258. . .

Explanation:

For cos 345 degrees, the angle 345° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 345° value = (√6 + √2)/4 or 0.9659258. . .
Since the cosine function is a periodic function, we can represent cos 345° as, cos 345 degrees = cos(345° + n × 360°), n ∈ Z.
⇒ cos 345° = cos 705° = cos 1065°, and so on.
Note: Since, cosine is an even function, the value of cos(-345°) = cos(345°).

Methods to Find Value of Cos 345 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 345° is given as 0.96592. . .. We can find the value of cos 345 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 345 Degrees Using Unit Circle

To find the value of cos 345 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 345° angle with the positive x-axis.
• The cos of 345 degrees equals the x-coordinate(0.9659) of the point of intersection (0.9659, -0.2588) of unit circle and r.

Hence the value of cos 345° = x = 0.9659 (approx)

Cos 345° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 345 degrees as:

• ± √(1-sin²(345°))
• ± 1/√(1 + tan²(345°))
• ± cot 345°/√(1 + cot²(345°))
• ±√(cosec²(345°) - 1)/cosec 345°
• 1/sec 345°

Note: Since 345° lies in the 4th Quadrant, the final value of cos 345° will be positive.

We can use trigonometric identities to represent cos 345° as,

• -cos(180° - 345°) = -cos(-165°)
• -cos(180° + 345°) = -cos 525°
• sin(90° + 345°) = sin 435°
• sin(90° - 345°) = sin(-255°)

☛ Also Check:

• cos 240 degrees
• cos 1 degrees
• cos 360 degrees
• cos 76 degrees
• cos 750 degrees
• cos 42 degrees

FAQs on Cos 345 Degrees

What is Cos 345 Degrees?

Cos 345 degrees is the value of cosine trigonometric function for an angle equal to 345 degrees. The value of cos 345° is (√6 + √2)/4 or 0.9659 (approx)

How to Find Cos 345° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 345° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(345°))
• ± 1/√(1 + tan²(345°))
• ± cot 345°/√(1 + cot²(345°))
• ± √(cosec²(345°) - 1)/cosec 345°
• 1/sec 345°

☛ Also check: trigonometry table

What is the Value of Cos 345° in Terms of Cosec 345°?

Since the cosine function can be represented using the cosecant function, we can write cos 345° as -[√(cosec²(345°) - 1)/cosec 345°]. The value of cosec 345° is equal to -3.86370.

How to Find the Value of Cos 345 Degrees?

The value of cos 345 degrees can be calculated by constructing an angle of 345° with the x-axis, and then finding the coordinates of the corresponding point (0.9659, -0.2588) on the unit circle. The value of cos 345° is equal to the x-coordinate (0.9659). ∴ cos 345° = 0.9659.

What is the Value of Cos 345 Degrees in Terms of Sin 345°?

Using trigonometric identities, we can write cos 345° in terms of sin 345° as, cos(345°) = √(1 - sin²(345°)). Here, the value of sin 345° is equal to -(√6 - √2)/4.