866 Words4 Pages

* Explain what a radian measure represents using the unit circle as a reference.
Pie is represented by a real number constant and is the ratio of the circumference of a circle to its diameter. Its value is approximately 3.14159. Since the circumference of the unit circle is 2 Pie, it is implied that the radian measure of an angle of one revolution is also 2 Pie. So the radian is the measure of how close a degree is to a complete circle.
* How do special right triangles directly relate to the unit circle?
There are two types of special right triangle, 90, 60, 30 and 45, 45, 90. With both triangles, the angles of degrees are directly related to the x and y values on the unit circle. With the case of 90, 60, 30 and 90, 45, 45, the angles are relative to the sin of its value on the unit circle. For an example, the sin of 30 degree is ½ and the sin of 60 degree is radical 3 over 2. Same with the special right triangle of 90, 45, 45, the sin of 45 is radical 2 over 2.
* Suppose that you did not have the unit circle on Circle A, but rather a circle of radius 5. Will the angle measures in degrees and/or radians change? Why or why not?
If the radius was to increase to 5, the angle measures will not change regardless. All the sin and cos values change but angle measurement will not be affected. This is because the revolution of a circle will always be 2 pie radians or 360 degree. Angle measures are the same in every circle as they are proportionate.
* Suppose that you did not have the unit circle on Circle A, but rather a circle of radius 5. What do you suppose the x- and y- coordinates will be for that circle in Quadrant 1?
As we know sin is relative to y and cos is relative to x. With this given, the x and y coordinates for a circle with a radius of 5 would simply be sin=y/radius and cos=x/ radius. This would apply to any circle with different radii.

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## Periodic Trends Assignment

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## Proof of Hero’s Formula

985 Words | 4 Pagesx and c-x, then the diagram looks as follows: The perpendicular has divided the triangle into two right-angled triangles. Now for any right-angle triangle, according to Pythagorean Theorem, [pic] = [pic] + [pic] If Pythagorean is applied to the right-angled triangles in the above triangle, then in the case of left right-angle triangle in the above diagram, it would give us the equation [pic] = [pic] + [pic] where ‘a’ = hypotenuse and ‘h’ = height/perpendicular and ‘x’ = base. Re-writing it, the equation would become which we will call Eq. A [pic] = [pic] - [pic] ---------------------( Eq. A Similarly, for the right angle triangle on the right half to triangle ABC, [pic] = [pic] + [pic] where ‘b’ = hypotenuse, ‘h’ = height/perpendicular and ‘c-x’ = base.

## Pythagorean Triples And Theorem Equation

891 Words | 4 PagesIt then has a right triangle, an triangle which has a one 90-degree angle. An example of an right angle could be seen as the corner of a piece of paper. The hypotenuse will be the longest side of the triangle. “The Pythagorean Theorem states that the square of the hypotenuse in right triangle is equal to the sum of the squares of the other two sides. This is expressed as a^2 + b^2 = c^2.” (Weisstien, 2011) 13 40 Pythagorean triangles are right triangles in which all three sides are integers.

## Law of Sines and Cosines

252 Words | 2 PagesWeek 5 Law of Sines and Cosines 1. Law of Sines: An equation to the length of all sides on a triangle and to the sines of its angles. 2. Law of Cosines: Related to the lengths of the sides of a plane triangle to the cosine of one of the angles. 3.

## Basic Geometric Terms and Definitions

548 Words | 3 PagesThe circles located on the inside are called inscribed circles, inscribed circles should touch each side of the triangle at a single point. The circles on the out sides are called circumscribed circles, the circumscribed circle touches each vertex of the triangle. There are also things called the incenter and the circumcenter. The incenter is the center of the inscribed circle and the circumcenter is the center of a circumscribed circle,the relation between a circle and a triangle is that circles can be located inside and outside a triangle. (5 points) |Score | | | 2.

## Trigonometry Essay Problem 1

1006 Words | 5 PagesCurrent as a function of time: Based upon the given information, we will be determining the Amplitude (A), period (and thus, B), and the phase shift (C). Given information states there is not a phase shift, therefore the value of D is zero and does not need to be recorded throughout the problem. The Amplitude (A) or maximum for the current has been given: 5 Amps. This indicates that the range will span from -5 to 5 on the y-axis. It is also given that at t=zero (time=zero) the current is equal to 5 Amps, meaning there is a negative phase shift (or phase shift to the left).

## Refraction Lab Essay

444 Words | 2 PagesNotice that the angle of incidence at the first surface is equal to the angle of refraction at the second surface. Prove algebraically (using Snell’s Law twice) why this is true. n1sin θ1=n2sin θ2 n2sin θ2=n1sin θ3 n1sin θ1=n1sin θ3 sin θ1=sin θ3 5. Do different colors refract at different angles? No, difference colors do not refract at different angles.

## 1.03 Module One

466 Words | 2 Pages5.Using complete sentences, describe to the Martians how to find the inverse of your function. Q5 answer: To find the inverse is just switching out 'y' and 'x', then solving for 'y'. So you would take the function f(x) = 2x + 5, put the 'y' in place of where the f(x) is. You now have y = 2x + 5. Switch out 'y' and 'x'.

## Lab 6: Centripetal Force And Torque

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## Week 2 Quiz

376 Words | 2 PagesThe first class in a relative frequency table is 50–59 and the corresponding relative frequency is 0.2. What does the 0.2 value indicate? Answer: 0.2 is equal to 1/5 or 20%, 0.2 indicates 20% of the data values are in this particular interval. 3. When you add the values 3, 5, 8, 12, and 20 and then divide by the number of values, the result is 9.6.

### Periodic Trends Assignment

478 Words | 2 Pages### Proof of Hero’s Formula

985 Words | 4 Pages### Pythagorean Triples And Theorem Equation

891 Words | 4 Pages### Law of Sines and Cosines

252 Words | 2 Pages### Basic Geometric Terms and Definitions

548 Words | 3 Pages### Trigonometry Essay Problem 1

1006 Words | 5 Pages### Refraction Lab Essay

444 Words | 2 Pages### 1.03 Module One

466 Words | 2 Pages### Lab 6: Centripetal Force And Torque

701 Words | 3 Pages### Week 2 Quiz

376 Words | 2 Pages