The Sine: The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse. We know the problem uses sin if it has 2 angles and one side lengths.
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. Tangent can be used to find the lengths and missing sides. This function is also be called TOA because Tan data is equal to opposite over adjacent.
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. The equation used for Cos data equals adjacent over hypotenuse and this formula can also be called CAH.
Arc Sine: A mathematical function that is the inverse of the sine function. The Formula used would be the data equals sin squared negative 1.
Arc Cosine: Function of x when -1≤x≤1. When the cosine of y is equal to x: cos y = x. Then the arc cosine of x is equal to the inverse cosine function of x, which is equal to y: arccosx = cos-1 x = y. The formula used would be Cos squared negative 1.
Law Sine: Provides a formula that relates the sides with the angles of a triangle. This formula allows you to relatively easily find the side length or the angle of any triangle.
Law Cosine: The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.. The formula I would use would be c squared equals a squared plus b squared - 2abcosC.
Learning in trigonometric I would start with the Pythagorean theorem and proving it (a^2+b^2=c^2.). An example of proving Pythagorean theory would be the hypotenuse being equal to the sum of the area of the shape. I used the Pythagorean theorem trying to figure out the unknown sides or angle of a right triangle. This is one of the relation between sine and cosine because this process follows the Pythagorean theorem. What this theorem does to trigonometric is it squared all three of the opposite, adjacent, and hypotenuse and adding the left hand side. Another thing I would use is for is the Pythagorean theorem would be to obtain the distance formula. The theorem connect to finding the distance formula because it sums the lengths of the shape is equaled to the length of the hypotenuse. I need to use the absolute value of the different coordinates while taking the square roots and we obtain the distance formula. By using the distance formula we can use it to obtain an equation that represent the circle. We would get the formula by the given coordinates in the center and any point around the circumference of the circle. Ones you get the equation it can be used on any other circle that comes up.
The unit circle was taught for us to get a better understanding of special angles like 30, 45, 60, etc... It also help us get a better visual and find things better like the exact value of ratios. A unit circle has ratio of 1 and a certain origin of (0,0). Important angles like 30, 45, and 60 can be remembered as sin, cos, and tan. The unit circle relates to cosine and sine because the points where the terminal side intersect with the unit circle X and Y. Sine would be defined as the Y and cosine as X. Tangent would be a straight line that would be on any curve at a given point, that straight line would just touch the point on the curve. The inverse angles were used to get angles from ratios of the circle and the formulas used would be Sin squared negative 1, Cos squared negative 1, and tan squared negative 1.