The period of tan(2x) is π/2 radians.
What is the period of sin2x?
The period of sin(2x) is π radians.
Sine normally takes 2π radians to repeat. But when you double the input (sin(2x)), the graph zooms through its cycle twice as fast. That’s why the period shrinks to π radians. Picture a vinyl record playing at 45 RPM instead of 33—it finishes the song in less time.
What is the period of the function y Tan2x?
The period of y = tan(2x) is π/2 radians.
Tangent’s basic rhythm is π radians per cycle. When you plug in 2x, you’re essentially doubling the tempo. The period gets cut in half to π/2. It’s the same math behind a sample in a DAW playing back at double speed—twice the loops in the same time.
What is period of TANX?
The period of tan(x) is π radians.
Unlike sine or cosine, tangent repeats every π radians. That’s because its vertical asymptotes are spaced π apart. Between each pair, the curve rockets from –∞ to +∞, then resets. After π radians, the next identical branch begins.
What’s the derivative of tan 2x?
The derivative of tan(2x) is 2·sec²(2x).
Hit it with the chain rule. Start with tan(u) → sec²(u), then multiply by u’ = 2. So dy/dx = 2 sec²(2x). If you blank out, just remember: tan’s derivative always brings sec² along for the ride.
What is the period of Cos 3x?
The period of cos(3x) is 2π/3 radians.
Cosine normally takes 2π radians to finish one cycle. When you triple the input (cos(3x)), the graph compresses horizontally. One full wave now fits into 2π/3 radians. Imagine a slinky squeezed to a third of its length—each coil repeats three times faster.
What is the period of Sinx TANX?
The product sin(x)·tan(x) has period 2π radians.
Sin(x) repeats every 2π, tan(x) every π. The smallest common interval? 2π. So their product repeats at 2π. Think of two dancers: one spins 360° while the other spins 180°. They only sync up after the 360° dancer completes her full turn.
What is cosine period?
The period of the cosine function is 2π radians.
Cosine’s signature move is a full hill-and-valley cycle every 2π radians. After that, the pattern repeats exactly. That 2π comes from the unit circle’s circumference—each radian maps back to the same (x,y) point.
What is the period of Y?
The period of y = 2 sin(x) is 2π radians.
Doubling the amplitude (from 1 to 2) cranks up the volume but doesn’t change the beat. Only the x-coefficient affects the period. Here, it’s still 1, so the cycle takes 2π radians. It’s like turning up the bass on a song—the tempo stays the same.
Is tan 2x equal to SEC 2x?
No, tan(2x) is not equal to sec(2x).
They’re related but not identical. From sec²(θ) – tan²(θ) = 1, you get sec(2x) = √(1 + tan²(2x)). That’s only equal to tan(2x) when tan(2x) = ±1. Otherwise, they’re distant cousins, not twins.
What is the derivative sin 2x?
The derivative of sin(2x) is 2 cos(2x).
Chain rule again. Derivative of sin(u) is cos(u), and u = 2x gives u’ = 2. Multiply them: 2 cos(2x). If you doubt it, remember: compressing the sine wave horizontally stretches its slope vertically by the same factor.
What is the period of Cos 5x?
The period of cos(5x) is 2π/5 radians.
Cosine’s default cycle is 2π radians. With 5x inside, the graph squeezes five times tighter. One full wave now takes just 2π/5 radians. It’s like a slinky compressed to one-fifth its length—each coil repeats five times faster.
What is the max value of sinx COSX?
The maximum value of sin(x)·cos(x) is ½.
Rewrite using the double-angle trick: sin(x)cos(x) = ½ sin(2x). Since sin(2x) maxes at 1, the product peaks at ½. That happens when 2x = π/2 + 2πn, so x = π/4 + πn. Graphically, sin(x) and cos(x) align perfectly at x = π/4 for the highest product.
What is the period wave?
The wave period is the time for two successive crests to pass a fixed point.
Stand on a pier and time the seconds between wave crests—that interval is the period, usually measured in seconds. A beach with a 6-second period? One new wave rolls in every six seconds. Oceanographers use this to rate surf conditions and predict wave energy.
Why is the period 2pi B?
The constant B in sin(Bx) or cos(Bx) sets the number of cycles per 2π; hence the period is 2π/B.
Unwrap the unit circle into a timeline. A full 360° (2π radians) span fits B cycles when the argument is Bx. So each cycle takes 2π/B radians. Sin(3x), for example, crams three full waves into the space where sin(x) has one. It’s a simple scaling trick you’ll see everywhere in trig.
