Cos 46 Degrees

The value of cos 46 degrees is 0.6946583. . .. Cos 46 degrees in radians is written as cos (46° × π/180°), i.e., cos (23π/90) or cos (0.802851. . .). In this article, we will discuss the methods to find the value of cos 46 degrees with examples.

• Cos 46°: 0.6946583. . .
• Cos (-46 degrees): 0.6946583. . .
• Cos 46° in radians: cos (23π/90) or cos (0.8028514 . . .)

What is the Value of Cos 46 Degrees?

The value of cos 46 degrees in decimal is 0.694658370. . .. Cos 46 degrees can also be expressed using the equivalent of the given angle (46 degrees) in radians (0.80285 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 46 degrees = 46° × (π/180°) rad = 23π/90 or 0.8028 . . .
∴ cos 46° = cos(0.8028) = 0.6946583. . .

Explanation:

For cos 46 degrees, the angle 46° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 46° value = 0.6946583. . .
Since the cosine function is a periodic function, we can represent cos 46° as, cos 46 degrees = cos(46° + n × 360°), n ∈ Z.
⇒ cos 46° = cos 406° = cos 766°, and so on.
Note: Since, cosine is an even function, the value of cos(-46°) = cos(46°).

Methods to Find Value of Cos 46 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 46° is given as 0.69465. . .. We can find the value of cos 46 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 46 Degrees Using Unit Circle

To find the value of cos 46 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 46° angle with the positive x-axis.
• The cos of 46 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 46° = x = 0.6947 (approx)

Cos 46° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 46 degrees as:

• ± √(1-sin²(46°))
• ± 1/√(1 + tan²(46°))
• ± cot 46°/√(1 + cot²(46°))
• ±√(cosec²(46°) - 1)/cosec 46°
• 1/sec 46°

Note: Since 46° lies in the 1st Quadrant, the final value of cos 46° will be positive.

We can use trigonometric identities to represent cos 46° as,

• -cos(180° - 46°) = -cos 134°
• -cos(180° + 46°) = -cos 226°
• sin(90° + 46°) = sin 136°
• sin(90° - 46°) = sin 44°

☛ Also Check:

• cos 135 degrees
• cos 20 degrees
• cos 18 degrees
• cos 41 degrees
• cos 600 degrees
• cos 110 degrees

FAQs on Cos 46 Degrees

What is Cos 46 Degrees?

Cos 46 degrees is the value of cosine trigonometric function for an angle equal to 46 degrees. The value of cos 46° is 0.6947 (approx)

How to Find the Value of Cos 46 Degrees?

The value of cos 46 degrees can be calculated by constructing an angle of 46° 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 46° is equal to the x-coordinate (0.6947). ∴ cos 46° = 0.6947.

How to Find Cos 46° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 46° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(46°))
• ± 1/√(1 + tan²(46°))
• ± cot 46°/√(1 + cot²(46°))
• ± √(cosec²(46°) - 1)/cosec 46°
• 1/sec 46°

☛ Also check: trigonometry table

What is the Value of Cos 46° in Terms of Sec 46°?

Since the secant function is the reciprocal of the cosine function, we can write cos 46° as 1/sec(46°). The value of sec 46° is equal to 1.439556.

What is the Value of Cos 46 Degrees in Terms of Cot 46°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 46° can be written as cot 46°/√(1 + cot²(46°)). Here, the value of cot 46° is equal to 0.96568.