Sec 150 Degrees

The value of Sec 150 degrees is -1.1547005. . .. Sec 150 degrees in radians is written as sec (150° × π/180°), i.e., sec (5π/6) or sec (2.617993. . .). In this article, we will discuss the methods to find the value of sec 150 degrees with examples.

• Sec 150°: -2/√3
• Sec 150° in decimal: -1.1547005. . .
• Sec (-150 degrees): -1.1547005. . . or -2/√3
• Sec 150° in radians: sec (5π/6) or sec (2.6179938 . . .)

What is the Value of Sec 150 Degrees?

The value of sec 150 degrees in decimal is -1.154700538. . .. Sec 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179 . . .
∴ sec 150° = sec(2.6179) = -2/√3 or -1.1547005. . .

Explanation:

For sec 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant). Since secant function is negative in the second quadrant, thus sec 150° value = -2/√3 or -1.1547005. . .
Since the secant function is a periodic function, we can represent sec 150° as, sec 150 degrees = sec(150° + n × 360°), n ∈ Z.
⇒ sec 150° = sec 510° = sec 870°, and so on.
Note: Since, secant is an even function, the value of sec(-150°) = sec(150°).

Methods to Find Value of Sec 150 Degrees

The secant function is negative in the 2nd quadrant. The value of sec 150° is given as -1.15470. . .. We can find the value of sec 150 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sec 150 Degrees Using Unit Circle

To find the value of sec 150 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis.
• The sec of 150 degrees equals the reciprocal of the x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.

Hence the value of sec 150° = 1/x = -1.1547 (approx)

Sec 150° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 150 degrees as:

• ± 1/√(1 - sin²(150°))
• ± √(1 + tan²(150°))
• ± √(1 + cot²(150°))/cot 150°
• ± cosec 150°/√(cosec²(150°) - 1)
• 1/cos 150°

Note: Since 150° lies in the 2nd Quadrant, the final value of sec 150° will be negative.

We can use trigonometric identities to represent sec 150° as,

• -sec(180° - 150°) = -sec 30°
• -sec(180° + 150°) = -sec 330°
• cosec(90° + 150°) = cosec 240°
• cosec(90° - 150°) = cosec(-60°)

☛ Also Check:

• sec 28 degrees
• sec 11 degrees
• sec 45 degrees
• sec 360 degrees
• sec 180 degrees
• sec 120 degrees

FAQs on Sec 150 Degrees

What is Sec 150 Degrees?

Sec 150 degrees is the value of secant trigonometric function for an angle equal to 150 degrees. The value of sec 150° is -2/√3 or -1.1547 (approx).

What is the Value of Sec 150 Degrees in Terms of Tan 150°?

We know, using trig identities, we can write sec 150° as -√(1 + tan²(150°)). Here, the value of tan 150° is equal to -0.5774.

How to Find Sec 150° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 150° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(150°))
• ± √(1 + tan²(150°))
• ± √(1 + cot²(150°))/cot 150°
• ± cosec 150°/√(cosec²(150°) - 1)
• 1/cos 150°

☛ Also check: trigonometry table

How to Find the Value of Sec 150 Degrees?

The value of sec 150 degrees can be calculated by constructing an angle of 150° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of sec 150° is equal to the reciprocal of the x-coordinate(-0.866). ∴ sec 150° = -1.1547.

What is the Value of Sec 150° in Terms of Cos 150°?

Since the cosine function is the reciprocal of the secant function, we can write sec 150° as 1/cos(150°). The value of cos 150° is equal to -0.866.