Cos 226 Degrees

The value of cos 226 degrees is -0.6946583. . .. Cos 226 degrees in radians is written as cos (226° × π/180°), i.e., cos (113π/90) or cos (3.944444. . .). In this article, we will discuss the methods to find the value of cos 226 degrees with examples.

• Cos 226°: -0.6946583. . .
• Cos (-226 degrees): -0.6946583. . .
• Cos 226° in radians: cos (113π/90) or cos (3.9444441 . . .)

What is the Value of Cos 226 Degrees?

The value of cos 226 degrees in decimal is -0.694658370. . .. Cos 226 degrees can also be expressed using the equivalent of the given angle (226 degrees) in radians (3.94444 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 226 degrees = 226° × (π/180°) rad = 113π/90 or 3.9444 . . .
∴ cos 226° = cos(3.9444) = -0.6946583. . .

Explanation:

For cos 226 degrees, the angle 226° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 226° value = -0.6946583. . .
Since the cosine function is a periodic function, we can represent cos 226° as, cos 226 degrees = cos(226° + n × 360°), n ∈ Z.
⇒ cos 226° = cos 586° = cos 946°, and so on.
Note: Since, cosine is an even function, the value of cos(-226°) = cos(226°).

Methods to Find Value of Cos 226 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 226° is given as -0.69465. . .. We can find the value of cos 226 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 226 Degrees Using Unit Circle

To find the value of cos 226 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 226° angle with the positive x-axis.
• The cos of 226 degrees equals the x-coordinate(-0.6947) of the point of intersection (-0.6947, -0.7193) of unit circle and r.

Hence the value of cos 226° = x = -0.6947 (approx)

Cos 226° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 226 degrees as:

• ± √(1-sin²(226°))
• ± 1/√(1 + tan²(226°))
• ± cot 226°/√(1 + cot²(226°))
• ±√(cosec²(226°) - 1)/cosec 226°
• 1/sec 226°

Note: Since 226° lies in the 3rd Quadrant, the final value of cos 226° will be negative.

We can use trigonometric identities to represent cos 226° as,

• -cos(180° - 226°) = -cos(-46°)
• -cos(180° + 226°) = -cos 406°
• sin(90° + 226°) = sin 316°
• sin(90° - 226°) = sin(-136°)

☛ Also Check:

• cos 20 degrees
• cos 240 degrees
• cos 2 degrees
• cos 1125 degrees
• cos 244 degrees
• cos 48 degrees

FAQs on Cos 226 Degrees

What is Cos 226 Degrees?

Cos 226 degrees is the value of cosine trigonometric function for an angle equal to 226 degrees. The value of cos 226° is -0.6947 (approx)

How to Find the Value of Cos 226 Degrees?

The value of cos 226 degrees can be calculated by constructing an angle of 226° with the x-axis, and then finding the coordinates of the corresponding point (-0.6947, -0.7193) on the unit circle. The value of cos 226° is equal to the x-coordinate (-0.6947). ∴ cos 226° = -0.6947.

What is the Value of Cos 226° in Terms of Cosec 226°?

Since the cosine function can be represented using the cosecant function, we can write cos 226° as [√(cosec²(226°) - 1)/cosec 226°]. The value of cosec 226° is equal to -1.39016.

What is the Value of Cos 226 Degrees in Terms of Tan 226°?

We know, using trig identities, we can write cos 226° as -1/√(1 + tan²(226°)). Here, the value of tan 226° is equal to 1.035530.

How to Find Cos 226° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 226° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(226°))
• ± 1/√(1 + tan²(226°))
• ± cot 226°/√(1 + cot²(226°))
• ± √(cosec²(226°) - 1)/cosec 226°
• 1/sec 226°

☛ Also check: trigonometry table