Sec 420 Degrees

The value of Sec 420 degrees is 2. Sec 420 degrees in radians is written as sec (420° × π/180°), i.e., sec (7π/3) or sec (7.330382. . .). In this article, we will discuss the methods to find the value of sec 420 degrees with examples.

• Sec 420°: 2
• Sec (-420 degrees): 2
• Sec 420° in radians: sec (7π/3) or sec (7.3303828 . . .)

What is the Value of Sec 420 Degrees?

The value of sec 420 degrees is 2. Sec 420 degrees can also be expressed using the equivalent of the given angle (420 degrees) in radians (7.33038 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 420 degrees = 420° × (π/180°) rad = 7π/3 or 7.3303 . . .
∴ sec 420° = sec(7.3303) = 2

Explanation:

For sec 420°, the angle 420° > 360°. Given the periodic property of the secant function, we can represent it as sec(420° mod 360°) = sec(60°). The angle 420°, coterminal to angle 60°, is located in the First Quadrant(Quadrant I).
Since secant function is positive in the 1st quadrant, thus sec 420 degrees value = 2
Similarly, sec 420° can also be written as, sec 420 degrees = (420° + n × 360°), n ∈ Z.
⇒ sec 420° = sec 780° = sec 1140°, and so on.
Note: Since, secant is an even function, the value of sec(-420°) = sec(420°).

Methods to Find Value of Sec 420 Degrees

The secant function is positive in the 1st quadrant. The value of sec 420° is given as 2. We can find the value of sec 420 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 420° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 420 degrees as:

• ± 1/√(1 - sin²(420°))
• ± √(1 + tan²(420°))
• ± √(1 + cot²(420°))/cot 420°
• ± cosec 420°/√(cosec²(420°) - 1)
• 1/cos 420°

Note: Since 420° lies in the 1st Quadrant, the final value of sec 420° will be positive.

We can use trigonometric identities to represent sec 420° as,

• -sec(180° - 420°) = -sec(-240°)
• -sec(180° + 420°) = -sec 600°
• cosec(90° + 420°) = cosec 510°
• cosec(90° - 420°) = cosec(-330°)

Sec 420 Degrees Using Unit Circle

To find the value of sec 420 degrees using the unit circle, represent 420° in the form (1 × 360°) + 60° [∵ 420°>360°] ∵ secant is a periodic function, sec 420° = sec 60°.

• Rotate ‘r’ anticlockwise to form 60° or 420° angle with the positive x-axis.
• The sec of 420 degrees equals the reciprocal of the x-coordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.

Hence the value of sec 420° = 1/x = 2

☛ Also Check:

• sec 390 degrees
• sec 70 degrees
• sec 75 degrees
• sec 45 degrees
• sec 11 degrees
• sec 28 degrees

FAQs on Sec 420 Degrees

What is Sec 420 Degrees?

Sec 420 degrees is the value of secant trigonometric function for an angle equal to 420 degrees. The value of sec 420° is 2.

What is the Value of Sec 420° in Terms of Cos 420°?

Since the cosine function is the reciprocal of the secant function, we can write sec 420° as 1/cos(420°). The value of cos 420° is equal to 0.5.

How to Find Sec 420° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 420° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(420°))
• ± √(1 + tan²(420°))
• ± √(1 + cot²(420°))/cot 420°
• ± cosec 420°/√(cosec²(420°) - 1)
• 1/cos 420°

☛ Also check: trigonometric table

What is the Value of Sec 420 Degrees in Terms of Sin 420°?

Using trigonometric identities, we can write sec 420° in terms of sin 420° as, sec(420°) = 1/√(1 - sin²(420°)). Here, the value of sin 420° is equal to 0.866.

How to Find the Value of Sec 420 Degrees?

The value of sec 420 degrees can be calculated by constructing an angle of 420° with the x-axis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of sec 420° is equal to the reciprocal of the x-coordinate(0.5). ∴ sec 420° = 2.