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Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Snell’s law (also known as the Snell–Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of ... more

Snell’s law (also known as the Snell–Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of ... more

To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by **20 degrees**. To do so, we first need to find the radius of this circle and the original angle.

Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:

To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get

While there are two angles that have this cosine value, the angle of **120.964** degrees is in the second quadrant as desired, so it is the angle we were looking for.

Rotating the point clockwise by **20 degrees**, the angle of the point will decrease to **100.964 degrees**. We can then evaluate the coordinates of the rotated point

For **x** axis:

For **y** axis:

The coordinates of the character on the rotated map will be **(-1.109, 5.725)**

Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen

http://www.opentextbookstore.com/precalc/

Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of the surface ... more

In physics, Bragg’s law, or Wulff–Bragg’s condition, a special case of Laue diffraction, gives the angles for coherent and incoherent ... more

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, ... more

In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. It is a four-sided figure in which ... more

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. In any convex quadrilateral ABCD, the ... more

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more

The beta angle is a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft ... more

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose ... more

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

The alpha helix (α-helix) is a common secondary structure of proteins and is a righthand-coiled or spiral conformation (helix). Residues in α-helices ... more

The minimum railway curve radius, the shortest allowable design radius for railway tracks under a particular set of conditions. It has an important bearing ... more

The capstan equation or belt friction equation, also known as Eytelwein’s formula, relates the hold-force to the load-force if a flexible line is ... more

calculates the speed of sliding of materials on a gravity conveyer

... more

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.The law of ... more

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In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates

(-3, 5). If the player rotates counterclockwise by20 degrees, then the objects in the map will correspondingly rotate20 degreesclockwise. Find the new coordinates of the character.