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1. What is Trigonometry?
Ans. Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of triangles. It involves the study of the ratios of the sides of a right-angled triangle and the various trigonometric functions such as sine, cosine, and tangent.
2. What are the important applications of Trigonometry?
Ans. Trigonometry finds its applications in various fields such as physics, engineering, astronomy, navigation, and architecture. It is used to calculate the height and distance of objects, to measure angles, and to solve problems related to waves and vibrations.
3. What is the Pythagorean Theorem and how is it related to Trigonometry?
Ans. The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Trigonometry is used to calculate the lengths of the sides of a right-angled triangle using the Pythagorean Theorem, and to find the angles of a triangle using the trigonometric functions.
4. What are the trigonometric ratios and how are they calculated?
Ans. The trigonometric ratios are the ratios of the sides of a right-angled triangle. The three basic trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). These ratios are calculated by dividing the length of one side of the triangle by the length of another side, as per the following formulas: sin (θ) = Opposite/Hypotenuse cos (θ) = Adjacent/Hypotenuse tan (θ) = Opposite/Adjacent
5. What is the unit circle and how is it used in Trigonometry?
Ans. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is used in Trigonometry to define the trigonometric functions for all angles, including those that are not acute angles. The coordinates of the points on the unit circle are used to calculate the values of the sine, cosine, and tangent of an angle. The unit circle also helps in visualizing and understanding the periodic nature of the trigonometric functions.
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