Trigonometry
Trigonometry derived from the Greek words “trigonon” (triangle) and “metron” (measure) Trigonometry is a branch of mathematic that deals with the relationships between the angles and sides of triangle. These trigonometric ratios can be seen easily in a unit circle. Unit circle is a fundamental concept in trigonometry. It is a circle with Radius of one unit and centered at the origin. The unit circle serves as a valuable too for understanding the geometric interpretations of trigonometric concepts and solving trigonometric equations and functions. Each point on the unit circle correspond to the value of trigonometric functions sine and cosine. Tangent lines to the unit circle correspond the value of trigonometric functions tangent, cotangent. In a unit circle x value of a point on the unit circle corresponds the value of trigonometric function of cosine. In a unit circle y value of a point on the unit circle corresponds the value of trigonometric function of sine. Pythagorean identity proves that;
In a right triangle sine function is the ratio between opposite side and hypotenuse.
In a right triangle cosine function is the ratio between adjacent side and hypotenuse.
Tangent function is the ratio between opposite side and adjacent side in a right triangle.
Identity of tangent is;
In trigonometry secant and cosecant functions are reciprocal form of cosine and sine functions.
When we combine reciprocal form and Pythagorean identity we end up with:
In IB MATH AA syllabus trigonometry is 3rd topic. SL section Trigonometry covers up to compound angle identities. But double angle identities are included. HL section trigonometry covers all chapters SL covers and extra covers compound angle identities.
You can find several formulas for trigonometry in IB Math data booklet. (link verebiliriz)
Trigonometry – sine rule
Trigonometry – cosine rule
Trigonometry – area of triangle
Trigonometry – identity for tanx
Trigonometry - Pythagorean identity
Trigonometry – Double angle identities
Trigonometry – Reciprocal trigonometric identities
Trigonometry – Compound angle identities.
You can find more key concepts in EduIB. There are many subtopics about trigonometry and mock exams in EduIB. Also keyconcepts about topic 3 trigonometry is very helpful for students. (key concepts link verebiliriz.)
Trigonometry has various application in fields such as physics, engineering, astronomy, architecture and many more. It helps in solving problems related to distances, heights, angles and periodic concepts such as oscillations and motion of objects in circular paths.
EduIB is a very good and rich question bank for probability questions.Also these trigonometry questions have detailed solutions at EduIB.
EduIB Questionbank gives you opportunity to solve real past paper like questions about Trigonometry. There is an example of one question about trigonometry which is very similar to question in IB May 2015 exam.
