The value of tan pi/2 is not defined. Tan pi/2 radians in degrees is written as tan ((π/2) × 180°/π), i.e., tung (90°). In this article, we will discuss the methods to find the value of tung pi/2 with examples.
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What is the Value of rã pi/2?
The value of tung pi/2 is not defined. Chảy pi/2 can also be expressed using the equivalent of the given angle (pi/2) in degrees (90°).
We know, using radian khổng lồ degree conversion, θ in degrees = θ in radians × (180°/pi)⇒ pi/2 radians = pi/2 × (180°/pi) = 90° or 90 degrees∴ chảy pi/2 = tan π/2 = tan(90°) = not defined
Explanation:
For tan pi/2, the angle pi/2 lies on the positive y-axis. Thus, rã pi/2 value = not definedSince the tangent function is a periodic function, we can represent chảy pi/2 as, rã pi/2 = tan(pi/2 + n × pi), n ∈ Z.⇒ tung pi/2 = tung 3pi/2 = tan 5pi/2 , & so on.Note: Since, tangent is an odd function, the value of tan(-pi/2) = -tan(pi/2) = undefined.
Methods lớn Find Value of rã pi/2
The value of tung pi/2 is given as not defined. We can find the value of chảy pi/2 by:
Using Trigonometric FunctionsUsing Unit CircleTan pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the rã pi/2 as:
sin(pi/2)/cos(pi/2)± sin(pi/2)/√(1 - sin²(pi/2))± √(1 - cos²(pi/2))/cos(pi/2)± 1/√(cosec²(pi/2) - 1)± √(sec²(pi/2) - 1)1/cot(pi/2)Note: Since pi/2 lies on the positive y-axis, the final value of chảy pi/2 is not defined.
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We can use trigonometric identities to lớn represent tan pi/2 as,
cot(pi/2 - pi/2) = cot 0-cot(pi/2 + pi/2) = -cot pi-tan (pi - pi/2) = -tan pi/2Tan pi/2 Using Unit Circle
To find the value of tan π/2 using the unit circle:
Rotate ‘r’ anticlockwise to size pi/2 angle with the positive x-axis.The tan of pi/2 equals the y-coordinate(1) divided by the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.Hence the value of rã pi/2 = y/x = not defined