Proving the Pythagorean Theorem
The pythagorean theorem is by definition is "is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides."
An example that we can use for proving the Pythagorean theory is that, The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs.
The pythagorean theorem is by definition is "is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides."
An example that we can use for proving the Pythagorean theory is that, The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs.
Using the Pythagorean Theorem to derive the Distance formula
According to the Pythagorean Theorem (|x2−x1|)2+(|y2−y1|)2=d2
We can drop the absolute value symbols since we are squaring the differences in the coordinates (the result will be positive).
(x2−x1)2+(y2−y1)2=d2
Taking the square root of both sides of the equation results in the distance formula.
d=√(x2−x1)2+(y2−y1)2
According to the Pythagorean Theorem (|x2−x1|)2+(|y2−y1|)2=d2
We can drop the absolute value symbols since we are squaring the differences in the coordinates (the result will be positive).
(x2−x1)2+(y2−y1)2=d2
Taking the square root of both sides of the equation results in the distance formula.
d=√(x2−x1)2+(y2−y1)2
Using the Distance Formula to derive the equation of a circle centered at the origin of a Cartesian coordinate plane
The Cartesian coordinate plane is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length." The equation that in the middle of the circle's origin of a Cartesian coordinate plane is
The Cartesian coordinate plane is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length." The equation that in the middle of the circle's origin of a Cartesian coordinate plane is
Define the Unit Circle
If a circle with centre starting at the origin (0,0) and the radius is one unit, its a unit circle. Finding points on the unit circle (30/60/90 degrees) I have a diagram to the far left which pinpoints all of the degrees. We received worksheets with finding the angles and points with using a protractor or using formulas. |
Using the symmetry of a circle to finding the points on the unit circle
In the diagram I have most pinpointed in the graph but a way to find the several different points all over the unit circle. In several worksheets it was more of discussing the ways of solving the angles than finding out serval ways to find them.
In the diagram I have most pinpointed in the graph but a way to find the several different points all over the unit circle. In several worksheets it was more of discussing the ways of solving the angles than finding out serval ways to find them.
Define the tangent function
The tangent faction is a function that can only be used on right triangles or acute angles. Tan(theta) = side opposite(Theta) over side adjacent to theata which equals y/x.
The tangent faction is a function that can only be used on right triangles or acute angles. Tan(theta) = side opposite(Theta) over side adjacent to theata which equals y/x.
Using the Unit circle to define the arcSine, arcCosine, and arcTangent function.
You can use the Unit circle to define the arcSine, arcCosine and arcTangent functions by putting in a degree into our functions. Take example lets go with thirty degrees, when using arcSine the answer is .5 . No other angle sin that produces .5 . The unit circle isn't heavily depended on finding these Arcs.
You can use the Unit circle to define the arcSine, arcCosine and arcTangent functions by putting in a degree into our functions. Take example lets go with thirty degrees, when using arcSine the answer is .5 . No other angle sin that produces .5 . The unit circle isn't heavily depended on finding these Arcs.
Using the Mount Everest problem to discover the Law of Sines ("taking apart")
In the Mount everest problem we had to take apart a triangle to find the a formula to use for the missing angle presented in the problem. In the end we got Law of Sine: SinB/b = SinA/a = SinC/c and our Law of Cosine: c^2=a^2+b^2-2abCos(theta)
In the Mount everest problem we had to take apart a triangle to find the a formula to use for the missing angle presented in the problem. In the end we got Law of Sine: SinB/b = SinA/a = SinC/c and our Law of Cosine: c^2=a^2+b^2-2abCos(theta)