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Cos 19 Degrees

The value of cos 19 degrees is 0.9455185. . .. Cos 19 degrees in radians is written as cos (19° × π/180°), i.e., cos (0.331612. . .). In this article, we will discuss the methods to find the value of cos 19 degrees with examples.

Cos 19°: 0.9455185. . .
Cos (-19 degrees): 0.9455185. . .
Cos 19° in radians: cos (0.3316125 . . .)

What is the Value of Cos 19 Degrees?

The value of cos 19 degrees in decimal is 0.945518575. . .. Cos 19 degrees can also be expressed using the equivalent of the given angle (19 degrees) in radians (0.33161 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 19 degrees = 19° × (π/180°) rad = 0.3316 . . .
∴ cos 19° = cos(0.3316) = 0.9455185. . .

Explanation:

For cos 19 degrees, the angle 19° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 19° value = 0.9455185. . .
Since the cosine function is a periodic function, we can represent cos 19° as, cos 19 degrees = cos(19° + n × 360°), n ∈ Z.
⇒ cos 19° = cos 379° = cos 739°, and so on.
Note: Since, cosine is an even function, the value of cos(-19°) = cos(19°).

Methods to Find Value of Cos 19 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 19° is given as 0.94551. . .. We can find the value of cos 19 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cos 19 Degrees Using Unit Circle

To find the value of cos 19 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 19° angle with the positive x-axis.
The cos of 19 degrees equals the x-coordinate(0.9455) of the point of intersection (0.9455, 0.3256) of unit circle and r.

Hence the value of cos 19° = x = 0.9455 (approx)

Cos 19° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 19 degrees as:

± √(1-sin²(19°))
± 1/√(1 + tan²(19°))
± cot 19°/√(1 + cot²(19°))
±√(cosec²(19°) - 1)/cosec 19°
1/sec 19°

Note: Since 19° lies in the 1st Quadrant, the final value of cos 19° will be positive.

We can use trigonometric identities to represent cos 19° as,

-cos(180° - 19°) = -cos 161°
-cos(180° + 19°) = -cos 199°
sin(90° + 19°) = sin 109°
sin(90° - 19°) = sin 71°

☛ Also Check:

Examples Using Cos 19 Degrees

Example 1: Using the value of cos 19°, solve: (1-sin²(19°)).

Solution:
We know, (1-sin²(19°)) = (cos²(19°)) = 0.894
⇒ (1-sin²(19°)) = 0.894
Example 2: Simplify: 9 (cos 19°/sin 109°)

Solution:

We know cos 19° = sin 109°
⇒ 9 cos 19°/sin 109° = 9 (cos 19°/cos 19°)
= 9(1) = 9
Example 3: Find the value of 2 cos(19°)/3 sin(71°).

Solution:

Using trigonometric identities, we know, cos(19°) = sin(90° - 19°) = sin 71°.
⇒ cos(19°) = sin(71°)
⇒ Value of 2 cos(19°)/3 sin(71°) = 2/3

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FAQs on Cos 19 Degrees

What is Cos 19 Degrees?

Cos 19 degrees is the value of cosine trigonometric function for an angle equal to 19 degrees. The value of cos 19° is 0.9455 (approx)

What is the Value of Cos 19 Degrees in Terms of Cot 19°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 19° can be written as cot 19°/√(1 + cot²(19°)). Here, the value of cot 19° is equal to 2.90421.

How to Find the Value of Cos 19 Degrees?

The value of cos 19 degrees can be calculated by constructing an angle of 19° with the x-axis, and then finding the coordinates of the corresponding point (0.9455, 0.3256) on the unit circle. The value of cos 19° is equal to the x-coordinate (0.9455). ∴ cos 19° = 0.9455.

How to Find Cos 19° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 19° can be given in terms of other trigonometric functions as:

± √(1-sin²(19°))
± 1/√(1 + tan²(19°))
± cot 19°/√(1 + cot²(19°))
± √(cosec²(19°) - 1)/cosec 19°
1/sec 19°

☛ Also check: trigonometry table

What is the Exact Value of cos 19 Degrees?

The exact value of cos 19 degrees can be given accurately up to 8 decimal places as 0.94551857.

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