Sec 70 Degrees

The value of Sec 70 degrees is 2.9238044. . .. Sec 70 degrees in radians is written as sec (70° × π/180°), i.e., sec (7π/18) or sec (1.221730. . .). In this article, we will discuss the methods to find the value of sec 70 degrees with examples.

• Sec 70° in decimal: 2.9238044. . .
• Sec (-70 degrees): 2.9238044. . .
• Sec 70° in radians: sec (7π/18) or sec (1.2217304 . . .)

What is the Value of Sec 70 Degrees?

The value of sec 70 degrees in decimal is 2.923804400. . .. Sec 70 degrees can also be expressed using the equivalent of the given angle (70 degrees) in radians (1.22173 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 70 degrees = 70° × (π/180°) rad = 7π/18 or 1.2217 . . .
∴ sec 70° = sec(1.2217) = 2.9238044. . .

Explanation:

For sec 70 degrees, the angle 70° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 70° value = 2.9238044. . .
Since the secant function is a periodic function, we can represent sec 70° as, sec 70 degrees = sec(70° + n × 360°), n ∈ Z.
⇒ sec 70° = sec 430° = sec 790°, and so on.
Note: Since, secant is an even function, the value of sec(-70°) = sec(70°).

Methods to Find Value of Sec 70 Degrees

The secant function is positive in the 1st quadrant. The value of sec 70° is given as 2.92380. . .. We can find the value of sec 70 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sec 70 Degrees Using Unit Circle

To find the value of sec 70 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 70° angle with the positive x-axis.
• The sec of 70 degrees equals the reciprocal of the x-coordinate(0.342) of the point of intersection (0.342, 0.9397) of unit circle and r.

Hence the value of sec 70° = 1/x = 2.9238 (approx)

Sec 70° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 70 degrees as:

• ± 1/√(1 - sin²(70°))
• ± √(1 + tan²(70°))
• ± √(1 + cot²(70°))/cot 70°
• ± cosec 70°/√(cosec²(70°) - 1)
• 1/cos 70°

Note: Since 70° lies in the 1st Quadrant, the final value of sec 70° will be positive.

We can use trigonometric identities to represent sec 70° as,

• -sec(180° - 70°) = -sec 110°
• -sec(180° + 70°) = -sec 250°
• cosec(90° + 70°) = cosec 160°
• cosec(90° - 70°) = cosec 20°

☛ Also Check:

• sec 135 degrees
• sec 120 degrees
• sec 30 degrees
• sec 270 degrees
• sec 180 degrees
• sec 11 degrees

FAQs on Sec 70 Degrees

What is Sec 70 Degrees?

Sec 70 degrees is the value of secant trigonometric function for an angle equal to 70 degrees. The value of sec 70° is 2.9238 (approx).

What is the Value of Sec 70 Degrees in Terms of Tan 70°?

We know, using trig identities, we can write sec 70° as √(1 + tan²(70°)). Here, the value of tan 70° is equal to 2.7475.

What is the Value of Sec 70° in Terms of Cosec 70°?

Since the secant function can be represented using the cosecant function, we can write sec 70° as [cosec 70°/√(cosec²(70°) - 1)]. The value of cosec 70° is equal to 1.0641.

How to Find Sec 70° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 70° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(70°))
• ± √(1 + tan²(70°))
• ± √(1 + cot²(70°))/cot 70°
• ± cosec 70°/√(cosec²(70°) - 1)
• 1/cos 70°

☛ Also check: trigonometry table

How to Find the Value of Sec 70 Degrees?

The value of sec 70 degrees can be calculated by constructing an angle of 70° with the x-axis, and then finding the coordinates of the corresponding point (0.342, 0.9397) on the unit circle. The value of sec 70° is equal to the reciprocal of the x-coordinate(0.342). ∴ sec 70° = 2.9238.