Trigonometry: Difference between revisions
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Trigonometry is a branch of [[mathematics]] that studies the relationships between the [[angles]] and side lengths of [[triangles]]. It is widely used in [[geometry]], [[astronomy]], [[physics]], [[engineering]], and [[navigation]], and provides essential tools for modeling periodic phenomena. | Trigonometry is a branch of [[mathematics]] that studies the relationships between the [[angles]] and side lengths of [[triangles]]. It is widely used in [[geometry]], [[astronomy]], [[physics]], [[engineering]], and [[navigation]], and provides essential tools for modeling periodic phenomena. | ||
== Pythagorean Theorem == | |||
One of the fundamentals of Trigonometry is Pythagorean theorem (or Pythagoras' theorem), named after ancient Greek [[Philosophy|philosopher]] and polymath Pythagoras. Pythagorean Theorem works only when one of the inner angles of the triangle is exactly 90 degrees ([[Angles|right angle]]). Pythagorean theorem then states that in this case, the side not touching the right angle, also said to be directly across from the right angle, which is named the hypotenuse, is equal to the square root of the sum of the squared side lengths. It is commonly rewritten as A² + B² = C², where A and B are the lengths of the lines that create the right angle, and C is the hypotenuse. | One of the fundamentals of Trigonometry is Pythagorean theorem (or Pythagoras' theorem), named after ancient Greek [[Philosophy|philosopher]] and polymath Pythagoras. Pythagorean Theorem works only when one of the inner angles of the triangle is exactly 90 degrees ([[Angles|right angle]]). Pythagorean theorem then states that in this case, the side not touching the right angle, also said to be directly across from the right angle, which is named the hypotenuse, is equal to the square root of the sum of the squared side lengths. It is commonly rewritten as A² + B² = C², where A and B are the lengths of the lines that create the right angle, and C is the hypotenuse. | ||
== Sine and Cosine == | |||
Regularly denoted sin and cos, Sine and Cosine are trigonometric functions of an angle. | |||
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cosA = adjacent / hypotenuse | cosA = adjacent / hypotenuse | ||
tanA = sinA / cosA = (opposite / hypotenuse) / (adjacent / hypotenuse) = opposite / adjacent | tanA = sinA / cosA = (opposite / hypotenuse) / (adjacent / hypotenuse) = opposite / adjacent | ||
Revision as of 09:01, 7 May 2025
Trigonometry is a branch of mathematics that studies the relationships between the angles and side lengths of triangles. It is widely used in geometry, astronomy, physics, engineering, and navigation, and provides essential tools for modeling periodic phenomena.
Pythagorean Theorem
One of the fundamentals of Trigonometry is Pythagorean theorem (or Pythagoras' theorem), named after ancient Greek philosopher and polymath Pythagoras. Pythagorean Theorem works only when one of the inner angles of the triangle is exactly 90 degrees (right angle). Pythagorean theorem then states that in this case, the side not touching the right angle, also said to be directly across from the right angle, which is named the hypotenuse, is equal to the square root of the sum of the squared side lengths. It is commonly rewritten as A² + B² = C², where A and B are the lengths of the lines that create the right angle, and C is the hypotenuse.
Sine and Cosine
Regularly denoted sin and cos, Sine and Cosine are trigonometric functions of an angle.
sinA = opposite / hypotenuse
cosA = adjacent / hypotenuse
tanA = sinA / cosA = (opposite / hypotenuse) / (adjacent / hypotenuse) = opposite / adjacent