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Sine and cosine rules, solving non-right-angled triangles, and applications.
Trigonometry is a branch of mathematics that deals with the relationships between the angles and side lengths of triangles. In Form 4, students will learn about the sine and cosine rules, how to solve non-right-angled triangles, and various applications in real-life scenarios.
Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the use of trigonometric functions such as sine, cosine, and tangent to solve problems involving right-angled triangles. The word 'trigonometry' comes from the Greek words 'tri' meaning three, 'gon' meaning angle, and 'metry' meaning measurement.
The sine rule states that in a triangle ABC, if sin(A) / a = sin(B) / b = sin(C) / c, then a / sin(A) = b / sin(B) = c / sin(C). The cosine rule states that in a triangle ABC, c^2 = a^2 + b^2 - 2ab * cos(C). These rules can be used to find the length of sides and the measure of angles in triangles.
The tangent rule states that in a triangle ABC, tan(A) = opposite side / adjacent side. This rule is useful for finding the ratio of the opposite side to the adjacent side in a right-angled triangle.
Trigonometry has many practical applications in fields such as navigation, physics, and engineering. For example, trigonometric functions are used in GPS systems to determine locations and distances. They are also used in the design of bridges and buildings to ensure stability and safety.
To solve a triangle, you need to know at least three pieces of information: two sides and one angle, or two angles and one side. You can use the sine, cosine, and tangent rules to find the missing values in the triangle.
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables. For example, sin^2(A) + cos^2(A) = 1 is a fundamental identity in trigonometry.
The graphs of trigonometric functions such as sine and cosine are periodic curves that repeat every 360 degrees. The amplitude, period, and phase shift can be used to describe the shape and position of these curves.
Calculators can be used to solve triangles by plugging in values for the sides and angles and using the calculator's trigonometric functions to find the missing values. This is a quick and efficient way to solve triangles.
What is trigonometry?
What is the sine rule used to find?
What is an example of a real-world application of trigonometry?
What is the cosine rule used to find?
What is the main difference between sine and cosine?
What is the tangent rule used to find?
What is the period of a sine function?
What is the amplitude of a cosine function?
What is the phase shift of a trigonometric function?
What is the formula for the sine of an angle?