Cos 42 Degrees

The value of cos 42 degrees is 0.7431448. . .. Cos 42 degrees in radians is written as cos (42° × π/180°), i.e., cos (7π/30) or cos (0.733038. . .). In this article, we will discuss the methods to find the value of cos 42 degrees with examples.

• Cos 42°: 0.7431448. . .
• Cos (-42 degrees): 0.7431448. . .
• Cos 42° in radians: cos (7π/30) or cos (0.7330382 . . .)

What is the Value of Cos 42 Degrees?

The value of cos 42 degrees in decimal is 0.743144825. . .. Cos 42 degrees can also be expressed using the equivalent of the given angle (42 degrees) in radians (0.73303 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 42 degrees = 42° × (π/180°) rad = 7π/30 or 0.7330 . . .
∴ cos 42° = cos(0.7330) = 0.7431448. . .

Explanation:

For cos 42 degrees, the angle 42° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 42° value = 0.7431448. . .
Since the cosine function is a periodic function, we can represent cos 42° as, cos 42 degrees = cos(42° + n × 360°), n ∈ Z.
⇒ cos 42° = cos 402° = cos 762°, and so on.
Note: Since, cosine is an even function, the value of cos(-42°) = cos(42°).

Methods to Find Value of Cos 42 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 42° is given as 0.74314. . .. We can find the value of cos 42 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 42 Degrees Using Unit Circle

To find the value of cos 42 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 42° angle with the positive x-axis.
• The cos of 42 degrees equals the x-coordinate(0.7431) of the point of intersection (0.7431, 0.6691) of unit circle and r.

Hence the value of cos 42° = x = 0.7431 (approx)

Cos 42° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 42 degrees as:

• ± √(1-sin²(42°))
• ± 1/√(1 + tan²(42°))
• ± cot 42°/√(1 + cot²(42°))
• ±√(cosec²(42°) - 1)/cosec 42°
• 1/sec 42°

Note: Since 42° lies in the 1st Quadrant, the final value of cos 42° will be positive.

We can use trigonometric identities to represent cos 42° as,

• -cos(180° - 42°) = -cos 138°
• -cos(180° + 42°) = -cos 222°
• sin(90° + 42°) = sin 132°
• sin(90° - 42°) = sin 48°

☛ Also Check:

• cos 11 degrees
• cos 45 degrees
• cos 40 degrees
• cos 25 degrees
• cos 73 degrees
• cos 315 degrees

FAQs on Cos 42 Degrees

What is Cos 42 Degrees?

Cos 42 degrees is the value of cosine trigonometric function for an angle equal to 42 degrees. The value of cos 42° is 0.7431 (approx)

What is the Value of Cos 42 Degrees in Terms of Tan 42°?

We know, using trig identities, we can write cos 42° as 1/√(1 + tan²(42°)). Here, the value of tan 42° is equal to 0.900404.

How to Find Cos 42° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 42° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(42°))
• ± 1/√(1 + tan²(42°))
• ± cot 42°/√(1 + cot²(42°))
• ± √(cosec²(42°) - 1)/cosec 42°
• 1/sec 42°

☛ Also check: trigonometric table

How to Find the Value of Cos 42 Degrees?

The value of cos 42 degrees can be calculated by constructing an angle of 42° with the x-axis, and then finding the coordinates of the corresponding point (0.7431, 0.6691) on the unit circle. The value of cos 42° is equal to the x-coordinate (0.7431). ∴ cos 42° = 0.7431.

What is the Value of Cos 42° in Terms of Cosec 42°?

Since the cosine function can be represented using the cosecant function, we can write cos 42° as [√(cosec²(42°) - 1)/cosec 42°]. The value of cosec 42° is equal to 1.49447.