Then, the formula for sin is \[\sin \theta = \frac{\text{Opposite Side} }{ \text{Hypothenuse} }\] What is sin equal to? Sin is a dimensionless amount, that measures the size of the inclination of an angle with respect to the horizontal reference, where the adjacent side is sitting...
Euler's Formula for Complex Equation: We can use Euler's identity to convert a complex trigonometric equation consisting of a real part and an imaginary into a complex exponential form. Euler's identity is given as: {eq}\displaystyle Ae^{\iota \theta}= A \left( ...
When there is a product of two different complex numbers written in trigonometric forms, then we'll convert these complex numbers into the exponential form using the general conversion formula and apply the product property of exponent...
In the given problem, we use the concept of trigonometry. In this problem, we use formulae like: {eq}\displaystyle \sin \theta = \sin \alpha \Rightarrow \theta = n\pi + (-1)^n \alpha, \text{where} \ n \in z {/eq} Answer and Explanation: Given: {eq}\displaystyle -5...
Power Series: Formula & Examples from Chapter 2 / Lesson 10 30K A power series is an infinite polynomial on the variable x and can be used to define a variety of functions. Explore the formula and examples of powe...
In the above integral, we can see there are four terms present integrand, integral sign, differential, and boundary values (upper and lower limit). The following formula helps us to solve the given definite integral. ∫qpz(x)dx=[Z(p)−Z(q)][Here,Z(x)istheantiderivativeofz(x)] ...
The derivative of an exponential function is computed by transforming the function into an exponential with base e, f(x)=ax=eln(ax)=exlna. Then, we employ the chain rule and the property for the derivative of an exponential with base e, d...
Note that we will not be getting a formula for the partial we see k in general, so we will be taking advantage of any shortcut that becomes available to us as we go. Answer and Explanation: We need four explicit derivatives. First, note that when...
Use Euler formula to derive the following identity: sin \beta \: cos \alpha = \frac{1}{2} sin(\alpha + \beta) - \frac{1}{2} sin(\alpha - \beta). Using Euler's formula, e^{i\theta}=\cos\theta+i\sin\theta prove the trigonometric identity \cos(4\theta)=...
Convert this equation to general form. y = -1(x + 2)^2 + 4 Find the given power. Write the answer in rectangular form. (2-2i)^5 Derive a formula for the left rectangular sum of f (x) = x^2 + 1 from 0 to 3. Fill in the missing components to rewrite each eq...