Perbandingan Trigonometri Pada Segitiga Siku-siku

Summary

This educational video explains trigonometric ratios in a right triangle, focusing on a triangle with sides AB = 24 cm and BC = 7 cm. The video covers how to calculate key trigonometric functions—sin, cos, tan, csc, sec, and cot—using the Pythagorean theorem and basic trigonometric formulas. Through step-by-step demonstrations, viewers learn how to find the hypotenuse and apply trigonometric relationships to solve for unknown values. The tutorial is designed to simplify trigonometry concepts and help students understand these essential mathematical principles for solving right triangle problems.

Takeaways

• 😀 Sin, Cos, Tan, Cosec, Sec, and Cot are the six main trigonometric ratios used in right-angled triangles.
• 😀 The 'opposite' side is the one directly in front of the angle, while the 'adjacent' side is beside the angle.
• 😀 The 'hypotenuse' is the longest side of a right-angled triangle, opposite the right angle.
• 😀 The formula for calculating Sin (θ) is 'opposite / hypotenuse'.
• 😀 Cos (θ) is calculated using the formula 'adjacent / hypotenuse'.
• 😀 Tan (θ) is found using the formula 'opposite / adjacent'.
• 😀 Cosec (θ) is the reciprocal of Sin, calculated as 'hypotenuse / opposite'.
• 😀 Sec (θ) is the reciprocal of Cos, calculated as 'hypotenuse / adjacent'.
• 😀 Cot (θ) is the reciprocal of Tan, calculated as 'adjacent / opposite'.
• 😀 To calculate the hypotenuse, use the Pythagorean theorem: 'hypotenuse = √(side₁² + side₂²)'.

Q & A

What is the primary focus of this script?

The primary focus is to explain how to calculate various trigonometric ratios (sin, cos, tan, cosec, sec, and cotan) for a right-angled triangle, specifically using an example where AB = 24 cm and BC = 7 cm.

What are the trigonometric ratios mentioned in the video?

The trigonometric ratios mentioned are sin (sine), cos (cosine), tan (tangent), cosec (cosecant), sec (secant), and cotan (cotangent).

How is the hypotenuse (AC) of the triangle calculated?

The hypotenuse (AC) is calculated using the Pythagorean theorem, which states that AC = √(AB² + BC²). For this example, AC = √(24² + 7²) = √625 = 25 cm.

What is the formula for sin(θ) in a right-angled triangle?

The formula for sin(θ) is sin(θ) = opposite/hypotenuse. In this case, sin(Alpha) = BC/AC = 7/25.

How is cos(θ) calculated in the example?

cos(θ) is calculated as cos(θ) = adjacent/hypotenuse. In this example, cos(Alpha) = AB/AC = 24/25.

What is the value of tan(Alpha) in the example?

The value of tan(Alpha) is calculated as tan(θ) = opposite/adjacent. Here, tan(Alpha) = BC/AB = 7/24.

How is cosec(Alpha) related to sin(Alpha)?

Cosec(Alpha) is the reciprocal of sin(Alpha), meaning cosec(θ) = 1/sin(θ). In this case, cosec(Alpha) = AC/BC = 25/7.

What does the sec(Alpha) represent in terms of cos(Alpha)?

Sec(Alpha) is the reciprocal of cos(Alpha), so sec(θ) = 1/cos(θ). For this example, sec(Alpha) = AC/AB = 25/24.

What is cotan(Alpha) and how is it calculated?

Cotan(Alpha) is the reciprocal of tan(Alpha), meaning cotan(θ) = 1/tan(θ). In this case, cotan(Alpha) = AB/BC = 24/7.

How can the trigonometric functions help in solving problems involving right-angled triangles?

Trigonometric functions help by relating the sides of a right-angled triangle to its angles. They provide a way to calculate unknown sides or angles, which is essential in solving various geometrical and physics problems.