Please donot use AI and give me step by step details for all. We come across periodic functions in our daily lives, from day and night cycles to events like sunset and sunrise, as well as the movement of planets. These phenomena of periodic functions provide insights into trigonometric functions. While we have explored the linear and curved functions, trigonometric functions delve into circular motions and rotations. These trigonometric concepts play a vital role in solving complex real-world problems, including architecture, structural design, space-related technologies, and more.

You are required to finish the 4 tasks in this assignment. You can use scientific calculators or online scientific calculators for this assignment. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool.?Show all steps wherever necessary.

Task 1:

After completing one revolution starting from the initial line, point A is observed to have coordinates(?23??,21?) on the unit circle. Using that information, please answer the following questions:

(i) Calculate all 6 values of the trigonometric functions (clearly state the formulae used to calculate these functions). (ii) Determine the quadrant in which the point lies and provide the reason. (iii) Calculate the angle formed by point A and the reference angle with the positive X-axis.

Task 2:

Alice had been standing on the ground (Point A) and observing a brightly colored object resembling a bird on the top of a tree at a distance of 4 meters from the tree. She decided to get a closer look by moving 2 meters closer to the tree (Point B). After moving closer, she realized that the object was not a bird but something that she could catch. Then, she decided to catch it by climbing the tree, which had a height of 6 meters from the ground.

Using the above scenario, please answer the following questions showing step by step calculations and stating the formulae.

(i) Find the angles formed by Alice at the points A and B relative to the top of the tree. What are these angles called as?

(ii) Determine whether angle A is larger than angle B. Make a conclusion about the comparison of angles when observing an object from a distance versus close.

(iii) Find the distances between the object and points A and B.

Task 3:

Answer the following questions by including the steps and formulas:

(a) Write the equation sine or cosine function with the given properties: Midline = 5, amplitude = 13, period =2? and phase shift =0

(b) For a trigonometric equation y = 15tan(?x/3+2) , find its stretching factor, period, phase shift, vertical asymptotes, and domain.

(c) Find the coordinates of points a, b, c, d, e and f on the following graph, stating the graph represents either a sine or cosine function.

360 -180 180 3600914 3 3 2 TT X Y=f(XX ) fi( )