 ### A traveling wave along the x-axis is given by the following wave function.

Here, $x$ and $Psi$ are measured in meters while $t$ is in seconds. Carefully study this wave equation and calculate the following quantities: [boldsymbol{ Psi(x,t)  = 4.8 cos ( 1.2x – 8.2t + 0.54 ) }] – Frequency ( in hertz ) – Wavelength ( in meters ) – Wave speed ( in meters per […]

### Write the first trigonometric function in terms of the second theta for in the given quadrant:

$cottheta$ $sintheta$ Where $theta$ in Quadrant II This problem aims to familiarize us with trigonometric functions. The concepts required to solve this problem are related to trigonometry, which includes quadrantal angles and signs of function. The sign of a trigonometric function such as $sintheta$ relies on the signs of the x,y coordinate points of the angle. We […]

### Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)

The aim of this problem is to get us familiar with the area of a very common quadrilateral known as a parallelogram. If we recall, a parallelogram is a pretty simple quadrilateral with two couples of parallel-faced sides. The opposite lengths of a parallelogram are of equal dimensions and the opposing angles of a parallelogram […]

### Find a vector function that represents the curve of intersection of the cylinder and the plane.

[Cylinder x^2+y^2=4] [Surface z=xy] The aim of this question is to find the vector function of the curve that is generated when a cylinder is intersected by a surface. The basic concept behind this article is the Vector-Valued Function and representation of different geometrical figures in parametric equations. A vector-valued function is defined as a […]

### Let P(x,y) be the terminal point on the unit circle determined by t. Then find the value for sin(t), cos(t) and tan(t).

The aim of this question is to find sin t, cos t, and tan t for a given point P=(x,y) on the unit circle which is determined by t. For this, we will be utilizing the Cartesian Coordinate system and Equation of Circle. The basic concept behind this question is the knowledge of the circle and its […]