Derivation of common trig functions and trig identities

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Hi, I am Gabrielle! I am an Actuarial and Applied Maths graduate student from the University of New South Wales in Sydney, Australia. I pursued my associate degree in Actuarial Science at Macquarie University afterward and now I have been working full time in the actuarial industry for almost 5 years. I love teaching and want to continue helping students enjoying Mathematics :) Mathematics has been one of my favorite subjects since high school and that's the reason why I am still excited to tutor in my spare time. I want to help students reach their best potential in Maths. When I was in junior high school, I started to give a lesson to a few of my friends in various subjects such as Science, Math, and Mandarin. It was the first step for me toward realizing that I love teaching. After I graduated from junior high school, I looked for a more challenging job, which was being a tutor outside the school environment. For two years, I taught students in general subjects but mostly in Mathematics. I got an opportunity after I graduated from senior high school to be an Assistant Teacher in one of the schools in my hometown. I was excited about that so I took that job during my holiday months. I was replaced in grades 10, 11, and 12 as a Maths Assistant Teacher, and it such an incredibly amazing experience for me. I graduated with a GPA of 9.3 from the UNSW Foundation Studies Program. I was a finalist in the Mathematics Olympiad Science National in 2009. I was also a finalist in the Astronomy Olympiad Science National in 2011.

Algebra Algebra introduces students to the fundamental concepts of variables, expressions, equations, and functions. This course focuses on simplifying expressions, solving linear and quadratic equations, and working with polynomials and inequalities. Students will also explore systems of equations, exponents, and factoring techniques. The course builds the foundation for higher-level mathematics and problem-solving skills applicable in various real-world contexts. Trigonometry Trigonometry delves into the relationships between the sides and angles of triangles, especially right triangles. The course covers the study of trigonometric functions (sine, cosine, tangent, and their reciprocals), their graphs, and applications in real-world scenarios, such as waves, circular motion, and physics problems. Additionally, students will learn how to solve trigonometric equations, apply identities, and understand the unit circle and radian measure. This course prepares students for advanced topics in calculus and science-related fields. Geometry Geometry focuses on the study of shapes, sizes, relative positions of figures, and the properties of space. Students will explore points, lines, planes, angles, circles, polygons, and three-dimensional figures, along with theorems and postulates that explain their relationships. The course emphasizes logical reasoning, proofs, congruence, similarity, area, volume, and coordinate geometry. Geometry strengthens problem-solving and spatial reasoning skills, which are essential in fields like architecture, engineering, and design.