Cos 145 Degrees

The value of cos 145 degrees is -0.8191520. . .. Cos 145 degrees in radians is written as cos (145° × π/180°), i.e., cos (29π/36) or cos (2.530727. . .). In this article, we will discuss the methods to find the value of cos 145 degrees with examples.

• Cos 145°: -0.8191520. . .
• Cos (-145 degrees): -0.8191520. . .
• Cos 145° in radians: cos (29π/36) or cos (2.5307274 . . .)

What is the Value of Cos 145 Degrees?

The value of cos 145 degrees in decimal is -0.819152044. . .. Cos 145 degrees can also be expressed using the equivalent of the given angle (145 degrees) in radians (2.53072 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 145 degrees = 145° × (π/180°) rad = 29π/36 or 2.5307 . . .
∴ cos 145° = cos(2.5307) = -0.8191520. . .

Explanation:

For cos 145 degrees, the angle 145° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 145° value = -0.8191520. . .
Since the cosine function is a periodic function, we can represent cos 145° as, cos 145 degrees = cos(145° + n × 360°), n ∈ Z.
⇒ cos 145° = cos 505° = cos 865°, and so on.
Note: Since, cosine is an even function, the value of cos(-145°) = cos(145°).

Methods to Find Value of Cos 145 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 145° is given as -0.81915. . .. We can find the value of cos 145 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 145° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 145 degrees as:

• ± √(1-sin²(145°))
• ± 1/√(1 + tan²(145°))
• ± cot 145°/√(1 + cot²(145°))
• ±√(cosec²(145°) - 1)/cosec 145°
• 1/sec 145°

Note: Since 145° lies in the 2nd Quadrant, the final value of cos 145° will be negative.

We can use trigonometric identities to represent cos 145° as,

• -cos(180° - 145°) = -cos 35°
• -cos(180° + 145°) = -cos 325°
• sin(90° + 145°) = sin 235°
• sin(90° - 145°) = sin(-55°)

Cos 145 Degrees Using Unit Circle

To find the value of cos 145 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 145° angle with the positive x-axis.
• The cos of 145 degrees equals the x-coordinate(-0.8192) of the point of intersection (-0.8192, 0.5736) of unit circle and r.

Hence the value of cos 145° = x = -0.8192 (approx)

☛ Also Check:

• cos 53 degrees
• cos 300 degrees
• cos 15 degrees
• cos 32 degrees
• cos 450 degrees
• cos 170 degrees

FAQs on Cos 145 Degrees

What is Cos 145 Degrees?

Cos 145 degrees is the value of cosine trigonometric function for an angle equal to 145 degrees. The value of cos 145° is -0.8192 (approx)

What is the Value of Cos 145° in Terms of Cosec 145°?

Since the cosine function can be represented using the cosecant function, we can write cos 145° as -[√(cosec²(145°) - 1)/cosec 145°]. The value of cosec 145° is equal to 1.74344.

How to Find the Value of Cos 145 Degrees?

The value of cos 145 degrees can be calculated by constructing an angle of 145° with the x-axis, and then finding the coordinates of the corresponding point (-0.8192, 0.5736) on the unit circle. The value of cos 145° is equal to the x-coordinate (-0.8192). ∴ cos 145° = -0.8192.

How to Find Cos 145° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 145° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(145°))
• ± 1/√(1 + tan²(145°))
• ± cot 145°/√(1 + cot²(145°))
• ± √(cosec²(145°) - 1)/cosec 145°
• 1/sec 145°

☛ Also check: trigonometry table

What is the Value of Cos 145 Degrees in Terms of Tan 145°?

We know, using trig identities, we can write cos 145° as -1/√(1 + tan²(145°)). Here, the value of tan 145° is equal to -0.700207.