Cos 38 Degrees

The value of cos 38 degrees is 0.7880107. . .. Cos 38 degrees in radians is written as cos (38° × π/180°), i.e., cos (19π/90) or cos (0.663225. . .). In this article, we will discuss the methods to find the value of cos 38 degrees with examples.

• Cos 38°: 0.7880107. . .
• Cos (-38 degrees): 0.7880107. . .
• Cos 38° in radians: cos (19π/90) or cos (0.6632251 . . .)

What is the Value of Cos 38 Degrees?

The value of cos 38 degrees in decimal is 0.788010753. . .. Cos 38 degrees can also be expressed using the equivalent of the given angle (38 degrees) in radians (0.66322 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 38 degrees = 38° × (π/180°) rad = 19π/90 or 0.6632 . . .
∴ cos 38° = cos(0.6632) = 0.7880107. . .

Explanation:

For cos 38 degrees, the angle 38° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 38° value = 0.7880107. . .
Since the cosine function is a periodic function, we can represent cos 38° as, cos 38 degrees = cos(38° + n × 360°), n ∈ Z.
⇒ cos 38° = cos 398° = cos 758°, and so on.
Note: Since, cosine is an even function, the value of cos(-38°) = cos(38°).

Methods to Find Value of Cos 38 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 38° is given as 0.78801. . .. We can find the value of cos 38 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 38 Degrees Using Unit Circle

To find the value of cos 38 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 38° angle with the positive x-axis.
• The cos of 38 degrees equals the x-coordinate(0.788) of the point of intersection (0.788, 0.6157) of unit circle and r.

Hence the value of cos 38° = x = 0.788 (approx)

Cos 38° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 38 degrees as:

• ± √(1-sin²(38°))
• ± 1/√(1 + tan²(38°))
• ± cot 38°/√(1 + cot²(38°))
• ±√(cosec²(38°) - 1)/cosec 38°
• 1/sec 38°

Note: Since 38° lies in the 1st Quadrant, the final value of cos 38° will be positive.

We can use trigonometric identities to represent cos 38° as,

• -cos(180° - 38°) = -cos 142°
• -cos(180° + 38°) = -cos 218°
• sin(90° + 38°) = sin 128°
• sin(90° - 38°) = sin 52°

☛ Also Check:

• cos 18 degrees
• cos 90 degrees
• cos 300 degrees
• cos 110 degrees
• cos 28 degrees
• cos 260 degrees

FAQs on Cos 38 Degrees

What is Cos 38 Degrees?

Cos 38 degrees is the value of cosine trigonometric function for an angle equal to 38 degrees. The value of cos 38° is 0.788 (approx)

How to Find the Value of Cos 38 Degrees?

The value of cos 38 degrees can be calculated by constructing an angle of 38° with the x-axis, and then finding the coordinates of the corresponding point (0.788, 0.6157) on the unit circle. The value of cos 38° is equal to the x-coordinate (0.788). ∴ cos 38° = 0.788.

What is the Value of Cos 38 Degrees in Terms of Tan 38°?

We know, using trig identities, we can write cos 38° as 1/√(1 + tan²(38°)). Here, the value of tan 38° is equal to 0.781285.

What is the Exact Value of cos 38 Degrees?

The exact value of cos 38 degrees can be given accurately up to 8 decimal places as 0.78801075.

How to Find Cos 38° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 38° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(38°))
• ± 1/√(1 + tan²(38°))
• ± cot 38°/√(1 + cot²(38°))
• ± √(cosec²(38°) - 1)/cosec 38°
• 1/sec 38°

☛ Also check: trigonometry table