Cos 32 Degrees

The value of cos 32 degrees is 0.8480480. . .. Cos 32 degrees in radians is written as cos (32° × π/180°), i.e., cos (8π/45) or cos (0.558505. . .). In this article, we will discuss the methods to find the value of cos 32 degrees with examples.

• Cos 32°: 0.8480480. . .
• Cos (-32 degrees): 0.8480480. . .
• Cos 32° in radians: cos (8π/45) or cos (0.5585053 . . .)

What is the Value of Cos 32 Degrees?

The value of cos 32 degrees in decimal is 0.848048096. . .. Cos 32 degrees can also be expressed using the equivalent of the given angle (32 degrees) in radians (0.55850 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 32 degrees = 32° × (π/180°) rad = 8π/45 or 0.5585 . . .
∴ cos 32° = cos(0.5585) = 0.8480480. . .

Explanation:

For cos 32 degrees, the angle 32° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 32° value = 0.8480480. . .
Since the cosine function is a periodic function, we can represent cos 32° as, cos 32 degrees = cos(32° + n × 360°), n ∈ Z.
⇒ cos 32° = cos 392° = cos 752°, and so on.
Note: Since, cosine is an even function, the value of cos(-32°) = cos(32°).

Methods to Find Value of Cos 32 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 32° is given as 0.84804. . .. We can find the value of cos 32 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 32 Degrees Using Unit Circle

To find the value of cos 32 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 32° angle with the positive x-axis.
• The cos of 32 degrees equals the x-coordinate(0.848) of the point of intersection (0.848, 0.5299) of unit circle and r.

Hence the value of cos 32° = x = 0.848 (approx)

Cos 32° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 32 degrees as:

• ± √(1-sin²(32°))
• ± 1/√(1 + tan²(32°))
• ± cot 32°/√(1 + cot²(32°))
• ±√(cosec²(32°) - 1)/cosec 32°
• 1/sec 32°

Note: Since 32° lies in the 1st Quadrant, the final value of cos 32° will be positive.

We can use trigonometric identities to represent cos 32° as,

• -cos(180° - 32°) = -cos 148°
• -cos(180° + 32°) = -cos 212°
• sin(90° + 32°) = sin 122°
• sin(90° - 32°) = sin 58°

☛ Also Check:

• cos 270 degrees
• cos 210 degrees
• cos 37 degrees
• cos 170 degrees
• cos 870 degrees
• cos 48 degrees

FAQs on Cos 32 Degrees

What is Cos 32 Degrees?

Cos 32 degrees is the value of cosine trigonometric function for an angle equal to 32 degrees. The value of cos 32° is 0.848 (approx)

What is the Value of Cos 32° in Terms of Sec 32°?

Since the secant function is the reciprocal of the cosine function, we can write cos 32° as 1/sec(32°). The value of sec 32° is equal to 1.179178.

How to Find the Value of Cos 32 Degrees?

The value of cos 32 degrees can be calculated by constructing an angle of 32° with the x-axis, and then finding the coordinates of the corresponding point (0.848, 0.5299) on the unit circle. The value of cos 32° is equal to the x-coordinate (0.848). ∴ cos 32° = 0.848.

What is the Value of Cos 32 Degrees in Terms of Sin 32°?

Using trigonometric identities, we can write cos 32° in terms of sin 32° as, cos(32°) = √(1 - sin²(32°)). Here, the value of sin 32° is equal to 0.5299.

How to Find Cos 32° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 32° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(32°))
• ± 1/√(1 + tan²(32°))
• ± cot 32°/√(1 + cot²(32°))
• ± √(cosec²(32°) - 1)/cosec 32°
• 1/sec 32°

☛ Also check: trigonometric table