"Measuring Our World"
Sine - the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.
SOH (Sin=o/h) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
Cosine - the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
CAH (cos=A/H) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
Tangent -a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.
TOA (tan=O/A) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
*The one hard thing for me with learning all the sines was which one was used for each equation/formula, because they all were alike.
ArcSine - a mathematical function that is the inverse of the sine function.
ArcSine was something that we barely scraped the surface of and was confusing to me. I learned that it not only found the sine of the triangle but also the angle of it.
ArcCosine - a mathematical function that is the inverse trigonometric function of cosine.
ArcCosine was something that we barely scraped the surface of and was confusing to me.I learned that it not only found the cosine of the triangle but also the angle of it.
ArcTangent - a mathematical function that is the inverse of the tangent function.
ArcTangent was something that we barely scraped the surface of and was confusing to me.I learned that it not only found the tangent of the triangle but also the angle of it.
Law of Sines -Law of sines is an equation relating the lengths of the sides of a triangle to the sines of its angles.
Law of Cosines - Law of cosines is the lengths of the sides of a triangle to the cosine of one of its angles.
We used law of cosines when we already knew two sides of the triangle.
SOH (Sin=o/h) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
Cosine - the trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
CAH (cos=A/H) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
Tangent -a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.
TOA (tan=O/A) This formula helped me learn/use the function after finding the adjacent, opposite, and hypotenuse of a right triangle
*The one hard thing for me with learning all the sines was which one was used for each equation/formula, because they all were alike.
ArcSine - a mathematical function that is the inverse of the sine function.
ArcSine was something that we barely scraped the surface of and was confusing to me. I learned that it not only found the sine of the triangle but also the angle of it.
ArcCosine - a mathematical function that is the inverse trigonometric function of cosine.
ArcCosine was something that we barely scraped the surface of and was confusing to me.I learned that it not only found the cosine of the triangle but also the angle of it.
ArcTangent - a mathematical function that is the inverse of the tangent function.
ArcTangent was something that we barely scraped the surface of and was confusing to me.I learned that it not only found the tangent of the triangle but also the angle of it.
Law of Sines -Law of sines is an equation relating the lengths of the sides of a triangle to the sines of its angles.
Law of Cosines - Law of cosines is the lengths of the sides of a triangle to the cosine of one of its angles.
We used law of cosines when we already knew two sides of the triangle.
Lots of explanations below
We kicked off the year with the Pythagorean theorem a2 + b2 = c2. Pretty much the formula helps us find the missing angle by plugging in the other two side lengths . C always represents the hypotenuse. We proved the Pythagorean theorem problem packet called “proof By Rugs”. We used our already known knowledge of right triangles to start the process of proving it, which is also a habit of a mathematician (starting small).From there we used the Pythagorean theorem to acquire the distance formula - (X2 + Y2 = r2). This equation is used to find the radius of any circle. With that you can now find the diameter of the circle. Then that is used to find the formula of a circle which is Pie time radius squared. After finishing the formulas we were asked to describe a circle with units. The circle had the radius we called 1 and points at certain spots around that had square roots and fractions for solving. After that we had to find points on the apex of the circle at 30 degrees, 45 degrees and 60 degrees. I was very confused on this part so I asked for help and kinda worked backwards from the answer to find each step. The next part we learned the cartesian coordinate plane and for me I think that this subject was the hardest for me. Dr Drew then asked us to find the points that were left by using symmetry in circles. After that we had to define this unit with cosine and sine. After learning sine and cosine we moved on to tangent(TOA), Which I kind of had previous knowledge of it but not enough to be a genius about it. From there we moved on to similarity and proportions which were kind of derived from cosine, sine, and tangent. we did a worksheet that had us use the operations sine, cosine, and tangent to complete it. Next was defining a unit circle with Arcsine, Arccosine, and of course Arctangent. We learned this subject mainly through presentations and worksheets based on missing side lengths etc. After that we learned about a cool experience the british had with mapping out Mt everest with only a protractor and a scope. They pretty much triangulated the height and distance from to points using Arcsine etc. And finally ending it we learned about deriving the law of cosine, sine, tangent etc. without right triangles and solving for missing sides and other parts of the triangles.