Sec 47 Degrees

The value of Sec 47 degrees is 1.4662791. . .. Sec 47 degrees in radians is written as sec (47° × π/180°), i.e., sec (0.820304. . .). In this article, we will discuss the methods to find the value of sec 47 degrees with examples.

• Sec 47° in decimal: 1.4662791. . .
• Sec (-47 degrees): 1.4662791. . .
• Sec 47° in radians: sec (0.8203047 . . .)

What is the Value of Sec 47 Degrees?

The value of sec 47 degrees in decimal is 1.466279185. . .. Sec 47 degrees can also be expressed using the equivalent of the given angle (47 degrees) in radians (0.82030 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 47 degrees = 47° × (π/180°) rad = 0.8203 . . .
∴ sec 47° = sec(0.8203) = 1.4662791. . .

Explanation:

For sec 47 degrees, the angle 47° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 47° value = 1.4662791. . .
Since the secant function is a periodic function, we can represent sec 47° as, sec 47 degrees = sec(47° + n × 360°), n ∈ Z.
⇒ sec 47° = sec 407° = sec 767°, and so on.
Note: Since, secant is an even function, the value of sec(-47°) = sec(47°).

Methods to Find Value of Sec 47 Degrees

The secant function is positive in the 1st quadrant. The value of sec 47° is given as 1.46627. . .. We can find the value of sec 47 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 47° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 47 degrees as:

• ± 1/√(1 - sin²(47°))
• ± √(1 + tan²(47°))
• ± √(1 + cot²(47°))/cot 47°
• ± cosec 47°/√(cosec²(47°) - 1)
• 1/cos 47°

Note: Since 47° lies in the 1st Quadrant, the final value of sec 47° will be positive.

We can use trigonometric identities to represent sec 47° as,

• -sec(180° - 47°) = -sec 133°
• -sec(180° + 47°) = -sec 227°
• cosec(90° + 47°) = cosec 137°
• cosec(90° - 47°) = cosec 43°

Sec 47 Degrees Using Unit Circle

To find the value of sec 47 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 47° angle with the positive x-axis.
• The sec of 47 degrees equals the reciprocal of the x-coordinate(0.682) of the point of intersection (0.682, 0.7314) of unit circle and r.

Hence the value of sec 47° = 1/x = 1.4663 (approx)

☛ Also Check:

• sec 90 degrees
• sec 390 degrees
• sec 120 degrees
• sec 47 degrees
• sec 180 degrees
• sec 60 degrees

FAQs on Sec 47 Degrees

What is Sec 47 Degrees?

Sec 47 degrees is the value of secant trigonometric function for an angle equal to 47 degrees. The value of sec 47° is 1.4663 (approx).

How to Find Sec 47° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 47° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(47°))
• ± √(1 + tan²(47°))
• ± √(1 + cot²(47°))/cot 47°
• ± cosec 47°/√(cosec²(47°) - 1)
• 1/cos 47°

☛ Also check: trigonometric table

What is the Exact Value of Sec 47 Degrees?

The exact value of sec 47 degrees can be given accurately up to 8 decimal places as 1.46627918.

What is the Value of Sec 47 Degrees in Terms of Cot 47°?

We can represent the secant function in terms of the cotangent function using trig identities, sec 47° can be written as √(1 + cot²(47°))/cot 47°. Here, the value of cot 47° is equal to 0.93252.

How to Find the Value of Sec 47 Degrees?

The value of sec 47 degrees can be calculated by constructing an angle of 47° with the x-axis, and then finding the coordinates of the corresponding point (0.682, 0.7314) on the unit circle. The value of sec 47° is equal to the reciprocal of the x-coordinate(0.682). ∴ sec 47° = 1.4663.