Sec 33 Degrees

The value of Sec 33 degrees is 1.1923632. . .. Sec 33 degrees in radians is written as sec (33° × π/180°), i.e., sec (11π/60) or sec (0.575958. . .). In this article, we will discuss the methods to find the value of sec 33 degrees with examples.

• Sec 33° in decimal: 1.1923632. . .
• Sec (-33 degrees): 1.1923632. . .
• Sec 33° in radians: sec (11π/60) or sec (0.5759586 . . .)

What is the Value of Sec 33 Degrees?

The value of sec 33 degrees in decimal is 1.192363292. . .. Sec 33 degrees can also be expressed using the equivalent of the given angle (33 degrees) in radians (0.57595 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 33 degrees = 33° × (π/180°) rad = 11π/60 or 0.5759 . . .
∴ sec 33° = sec(0.5759) = 1.1923632. . .

Explanation:

For sec 33 degrees, the angle 33° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 33° value = 1.1923632. . .
Since the secant function is a periodic function, we can represent sec 33° as, sec 33 degrees = sec(33° + n × 360°), n ∈ Z.
⇒ sec 33° = sec 393° = sec 753°, and so on.
Note: Since, secant is an even function, the value of sec(-33°) = sec(33°).

Methods to Find Value of Sec 33 Degrees

The secant function is positive in the 1st quadrant. The value of sec 33° is given as 1.19236. . .. We can find the value of sec 33 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sec 33 Degrees Using Unit Circle

To find the value of sec 33 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 33° angle with the positive x-axis.
• The sec of 33 degrees equals the reciprocal of the x-coordinate(0.8387) of the point of intersection (0.8387, 0.5446) of unit circle and r.

Hence the value of sec 33° = 1/x = 1.1924 (approx)

Sec 33° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 33 degrees as:

• ± 1/√(1 - sin²(33°))
• ± √(1 + tan²(33°))
• ± √(1 + cot²(33°))/cot 33°
• ± cosec 33°/√(cosec²(33°) - 1)
• 1/cos 33°

Note: Since 33° lies in the 1st Quadrant, the final value of sec 33° will be positive.

We can use trigonometric identities to represent sec 33° as,

• -sec(180° - 33°) = -sec 147°
• -sec(180° + 33°) = -sec 213°
• cosec(90° + 33°) = cosec 123°
• cosec(90° - 33°) = cosec 57°

☛ Also Check:

• sec 90 degrees
• sec 390 degrees
• sec 360 degrees
• sec 420 degrees
• sec 225 degrees
• sec 405 degrees

FAQs on Sec 33 Degrees

What is Sec 33 Degrees?

Sec 33 degrees is the value of secant trigonometric function for an angle equal to 33 degrees. The value of sec 33° is 1.1924 (approx).

What is the Value of Sec 33 Degrees in Terms of Sin 33°?

Using trigonometric identities, we can write sec 33° in terms of sin 33° as, sec(33°) = 1/√(1 - sin²(33°)). Here, the value of sin 33° is equal to 0.5446.

How to Find the Value of Sec 33 Degrees?

The value of sec 33 degrees can be calculated by constructing an angle of 33° with the x-axis, and then finding the coordinates of the corresponding point (0.8387, 0.5446) on the unit circle. The value of sec 33° is equal to the reciprocal of the x-coordinate(0.8387). ∴ sec 33° = 1.1924.

What is the Exact Value of Sec 33 Degrees?

The exact value of sec 33 degrees can be given accurately up to 8 decimal places as 1.19236329.

How to Find Sec 33° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 33° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(33°))
• ± √(1 + tan²(33°))
• ± √(1 + cot²(33°))/cot 33°
• ± cosec 33°/√(cosec²(33°) - 1)
• 1/cos 33°

☛ Also check: trigonometric table