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Cos 48 Degrees

The value of cos 48 degrees is 0.6691306. . .. Cos 48 degrees in radians is written as cos (48° × π/180°), i.e., cos (4π/15) or cos (0.837758. . .). In this article, we will discuss the methods to find the value of cos 48 degrees with examples.

Cos 48°: 0.6691306. . .
Cos (-48 degrees): 0.6691306. . .
Cos 48° in radians: cos (4π/15) or cos (0.8377580 . . .)

What is the Value of Cos 48 Degrees?

The value of cos 48 degrees in decimal is 0.669130606. . .. Cos 48 degrees can also be expressed using the equivalent of the given angle (48 degrees) in radians (0.83775 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 48 degrees = 48° × (π/180°) rad = 4π/15 or 0.8377 . . .
∴ cos 48° = cos(0.8377) = 0.6691306. . .

Explanation:

For cos 48 degrees, the angle 48° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 48° value = 0.6691306. . .
Since the cosine function is a periodic function, we can represent cos 48° as, cos 48 degrees = cos(48° + n × 360°), n ∈ Z.
⇒ cos 48° = cos 408° = cos 768°, and so on.
Note: Since, cosine is an even function, the value of cos(-48°) = cos(48°).

Methods to Find Value of Cos 48 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 48° is given as 0.66913. . .. We can find the value of cos 48 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cos 48° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 48 degrees as:

± √(1-sin²(48°))
± 1/√(1 + tan²(48°))
± cot 48°/√(1 + cot²(48°))
±√(cosec²(48°) - 1)/cosec 48°
1/sec 48°

Note: Since 48° lies in the 1st Quadrant, the final value of cos 48° will be positive.

We can use trigonometric identities to represent cos 48° as,

-cos(180° - 48°) = -cos 132°
-cos(180° + 48°) = -cos 228°
sin(90° + 48°) = sin 138°
sin(90° - 48°) = sin 42°

Cos 48 Degrees Using Unit Circle

To find the value of cos 48 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 48° angle with the positive x-axis.
The cos of 48 degrees equals the x-coordinate(0.6691) of the point of intersection (0.6691, 0.7431) of unit circle and r.

Hence the value of cos 48° = x = 0.6691 (approx)

☛ Also Check:

Examples Using Cos 48 Degrees

Example 1: Simplify: 8 (cos 48°/sin 138°)

Solution:

We know cos 48° = sin 138°
⇒ 8 cos 48°/sin 138° = 8 (cos 48°/cos 48°)
= 8(1) = 8
Example 2: Using the value of cos 48°, solve: (1-sin²(48°)).

Solution:
We know, (1-sin²(48°)) = (cos²(48°)) = 0.4477
⇒ (1-sin²(48°)) = 0.4477
Example 3: Find the value of (cos² 24° - sin² 24°). [Hint: Use cos 48° = 0.6691]

Solution:

Using the cos 2a formula,
(cos² 24° - sin² 24°) = cos(2 × 24°) = cos 48°
∵ cos 48° = 0.6691
⇒ (cos² 24° - sin² 24°) = 0.6691

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FAQs on Cos 48 Degrees

What is Cos 48 Degrees?

Cos 48 degrees is the value of cosine trigonometric function for an angle equal to 48 degrees. The value of cos 48° is 0.6691 (approx)

How to Find the Value of Cos 48 Degrees?

The value of cos 48 degrees can be calculated by constructing an angle of 48° with the x-axis, and then finding the coordinates of the corresponding point (0.6691, 0.7431) on the unit circle. The value of cos 48° is equal to the x-coordinate (0.6691). ∴ cos 48° = 0.6691.

How to Find Cos 48° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 48° can be given in terms of other trigonometric functions as:

± √(1-sin²(48°))
± 1/√(1 + tan²(48°))
± cot 48°/√(1 + cot²(48°))
± √(cosec²(48°) - 1)/cosec 48°
1/sec 48°

☛ Also check: trigonometry table

What is the Value of Cos 48 Degrees in Terms of Sin 48°?

Using trigonometric identities, we can write cos 48° in terms of sin 48° as, cos(48°) = √(1 - sin²(48°)). Here, the value of sin 48° is equal to 0.7431.

What is the Exact Value of cos 48 Degrees?

The exact value of cos 48 degrees can be given accurately up to 8 decimal places as 0.66913060.

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