Use the form acos(bx−c)+ d a cos (b x - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude |a| | a |. Find the period of 4cos(2x) 4 cos (2 x). Tap for more steps... Find the phase shift using the formula c b c b. Tap for more steps...

To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for …

Replace all occurrences of u u with 2x 2 x. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

2025年3月24日 · Take the square root: After isolating cos^2 (2x), we take the square root of both sides, remembering to consider both positive and negative roots. Solve for the angle: We solve for 2x using the inverse cosine function (arccos or cos^-1).

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Finding Solutions for x: Find the values of x that satisfy the obtained values of sin x within the desired interval (usually 0 to 2π, unless otherwise specified). The given equation is 4cos²x - 3sin x = 3. Let y = sin x. The equation becomes: So, y = 1/4 or y = -1. Therefore, sin x = 1/4 or sin x = -1.

Solving for x in a trigonometric equation involving the cosine function. Isolate the cosine function: Divide both sides of the equation by 4 to isolate the cos (2x) term. Find the general solution for the angle: Determine the angles whose cosine is equal to the value obtained in step 1.

Since θ =2x, we get that dθ = 2dx. Hence you have to use the chain rule for differentiation. So the calculations become, on using chain rule (marked in red): dxd (sin2x)= dθd (sinθ)⋅dxdθ = cosθ⋅2 = 2cos2x ...

Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude . Find the period of . Tap for more steps... The period of the function can be …

2016年10月21日 · How do you solve 4 cos2 x − 1 = 0? x = ± 4π 3, ± 2π 3, ± 5π 3, ± π 3. This is a trivial quadratic equation in cosx. In order to solve this you need to be familiar with the graphs of the trig functions along with common values: The range of soutions is not specified in the question, so lets assume we want a solutio in radians, and −2π ≤ x ≤ 2π.