Question

Evaluate 3 tan 2pi/3, - 2 sec 3pi/4 with teignometric methord

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Answer 1

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Sec 3pi/4

The value of sec 3pi/4 is -1.4142135. . .. Sec 3pi/4 radians in degrees is written as sec ((3π/4) × 180°/π), i.e., sec (135°). In this article, we will discuss the methods to find the value of sec 3pi/4 with examples.

Sec 3pi/4: -√2

Sec 3pi/4 in decimal: -1.4142135. . .

Sec (-3pi/4): -1.4142135. . . or -√2

Sec 3pi/4 in degrees: sec (135°)

What is the Value of Sec 3pi/4?

The value of sec 3pi/4 in decimal is -1.414213562. . .. Sec 3pi/4 can also be expressed using the equivalent of the given angle (3pi/4) in degrees (135°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)

⇒ 3pi/4 radians = 3pi/4 × (180°/pi) = 135° or 135 degrees

∴ sec 3pi/4 = sec 3π/4 = sec(135°) = -√2 or -1.4142135. . .

Sec 3pi/4

Explanation:

For sec 3pi/4, the angle 3pi/4 lies between pi/2 and pi (Second Quadrant). Since secant function is negative in the second quadrant, thus sec 3pi/4 value = -√2 or -1.4142135. . .

Since the secant function is a periodic function, we can represent sec 3pi/4 as, sec 3pi/4 = sec(3pi/4 + n × 2pi), n ∈ Z.

⇒ sec 3pi/4 = sec 11pi/4 = sec 19pi/4 , and so on.

Note: Since, secant is an even function, the value of sec(-3pi/4) = sec(3pi/4).