sin2x = 2 * cos(x - π/2) 三、sin2x的泰勒级数展开 根据二项式定理,我们可以将cos(x - π/2)展开为: cos(x - π/2) = 1 - (x - π/2)^2 / 2! + (x - π/2)^4 / 4! - (x - π/2)^6 / 6! + ... 将上式乘以2,得到: sin2x = 2 * (1 - (x - π/2)^2 / ...
sin(2x) ≈ sin(0) + 2cos(0)(x - 0) = 0 + 2 * 1 = 2 因此,sin(2x) 的近似值为 2。 2.求解相关问题 泰勒公式还可以用于求解一些与sin(2x) 相关的问题。例如,我们可以利用泰勒公式求解 sin(2x) 在一定区间上的最大值、最小值等。不过,需要注意的是,泰勒公式在一定区间上的精度是有限的,因...
Finding the Slope: We can determine the slope by differentiating the function with respect to the variable at the indicated point. The formula is {eq}\displaystyle m= \frac{dy}{dx} {/eq}. where {eq}\displaystyle m {/eq} is the slope. We have to appl...
Answer and Explanation: Become a Study.com member to unlock this answer! Create your account View this answer The given equation is sin2x(tanx+cotx)=2. Use the double-angle formula sin2x=2sinxcosx on the left-hand side of... See full answer below.Bec...
{eq}\int \cos^2 x \sin 2x \, \mathrm{d}x {/eq} Integration by Substitution: Integral by substitution is the method of integration applied to solve an unknown integral. By this method, an unknown integral can be converted into an integral that we know how to solve. The formula of in...
\frac{{\rm{d}}\sin (-2x)}{{\rm{d}}x}&=-2\cos (2x)\end{align}\\此即为所求的答案...
sin2x+cos2x=1Substituting the value of cosx:sin2x+(−35)2=1sin2x+925=1sin2x=1−925sin2x=2525−925=1625Taking the square root, we find:sinx=√1625=45Since x is in the second quadrant, sinx is positive:sinx=45 Step 2: Find sin2x Using the double angle formula for sine:sin2x...
Now, we need to factor or use the quadratic formula to solve for t. The factors of the equation are:(5t−2)(t−1)=0Setting each factor to zero gives us:5t−2=0⇒t=25t−1=0⇒t=1 Step 6: Solve for cos2xRecall that t=2cos2x. We now have two cases to consider: 1...
cos（-2x）
cos x cos2x-2sin xsin 2xEquate derivative to zero and use double angle formulaeRemove factor of cos x and reduce equation to one in a single trig functionObtain 6sin² x = 1, 6cos² x = 5 or 5tan²x = 1Solve and obtain x=0.421[Alternative : Use double angle formula M1....