What are the important points to graph y=sin 2x? | Socratic
Apr 17, 2018 · The equation is y = sin2x, so it is in the form y = sin(b ⋅ x) The period of this graph is 2π b, which equals 2π 2 or π. Therefore, the "important points" (quarter points) when graphing this function will be π 4 apart. The amplitude of this graph is 1, and there are no phase or vertical shifts, so the midline will be 0, maximum 1, and ...
What is the graph of y=sin^2 x? - Socratic
Mar 23, 2015 · Here is the graph: graph{(sinx)^2 [-10, 10, -5, 5]} Recall the double-angle formula for cosine: cos(2x) = 1-2sin^2(x) Subtract 1 from both sides: cos(2x) -1 = -2sin^2(x) Divide both sides by -2 -1/2cos(2x) + 1/2 You now have a standard cosine equation with Amplitude = 1/2 Period = pi Vertical Shift = up by 1/2 Something important to recognize, if you compare this to …
How do you graph y = sin 2x? - Socratic
Jun 14, 2017 · Explanation: y = sin(2x) AMPLITUDE: 2. PERIOD: 2π. HORIZONTAL SHIFTS: none. VERTICAL SHIFTS: none. TYPE: sine graph. AMPLITUDE = distance from middle of graph (y=0) to highest and lowest points on graph. PERIOD = interval in which the graph repeats itself (every 2π, the graph will repeat its pattern.
How do you graph y=sin2x? - Socratic
Aug 9, 2018 · Therefore, y = sin2x is basically the y = sinx graph but instead of having a period of 2π, it has a period of π. So what that means is that in y = sin2x, you will see two sinx graphs occurring. graph {sin (2x) [-10, 10, -5, 5]} Below When written in the form y=asin (nx+b)+c where a is the amplitude n is used to find the period of the function ...
How do you graph #y = -sin(2x)#? - Socratic
Jun 15, 2015 · These are three steps (transformations) that you can apply in every order you want,and you'll obtain y=-sin (2x). 1. Start graphing the trig function you know, y=sin (x). graph {sinx [-10, 10, -5, 5]} Doubling the argument you have a compression in the period, that means that the function double the frequency: if we had the solutions in 0,pi ...
How do you prove #sin^2x + cos^2x = 1#? - Socratic
Feb 13, 2017 · So for example: sin2(θ +π) +cos2(θ + π) = (−sinθ)2 +(−cosθ)2 = sin2θ +cos2θ = 1. Pythagoras theorem. Given a right angled triangle with sides a, b and c consider the following diagram: The area of the large square is (a +b)2. The area of the small, tilted square is c2. The area of each triangle is 1 2 ab. So we have:
How do you find the domain and range of #y = sin(2x)#? - Socratic
Oct 25, 2017 · Domain: (-oo, +oo) Range: [-1, +1] y=sin(2x) y is defined forall x in RR :. the domain of y is (-oo, +oo) Let theta = 2x y = sin theta -> -1<= y <= +1 forall theta in RR Hence, y = sin(2x) -> -1<= y <= +1 forall theta in RR :. the range of y is [-1, +1] We can observe the domain and range of y from the graph of #y=sin(2x) below. graph{sin(2x) [-6.25, 6.234, -3.12, 3.124]}
How do you find the points where the graph of the function
Mar 15, 2016 · Horizontal tangent means neither increasing nor decreasing. Specifically, the derivative of the function has to be zero f'(x)=0. f(x)=sin(2x)+sin^2x f'(x)=cos(2x)(2x)'+2sinx*(sinx)' f'(x)=2cos(2x)+2sinxcosx Set f'(x)=0 0=2cos(2x)+2sinxcosx 2sinxcosx=-2cos(2x) sin(2x)=-2cos(2x) sin(2x)/cos(2x)=-2 tan(2x)=-2 2x=arctan(2) x=(arctan(2))/2 x=0.5536 This is one …
Find all points on graph of f(x)=2sinx+sin^2x where slope = 0
Jul 27, 2008 · Yes, you can use a graphing calculator to find the points where the slope is 0. Simply graph the function f (x)=2sinx+sin^2x and use the calculator's intersection or zeros feature to find the x-values where the graph intersects the x-axis. These x-values correspond to the points where the slope is 0.
General Sinusoidal Graphs - Trigonometry - Socratic
Example: Describe the transformations to get g(x) = 2sin(3(x + π 4)) + 2 from f (x) = sinx. Here are what each of the parameters in the equation y = asin(b(x − c)) +d: a → vertical stretch. 1 b → horizontal stretch. c → phase shift. d → vertical transformation. So in the given equation, we have a vertical stretch by a factor of 2, a ...