Video Pembelajaran Perbandingan Trigonometri Kelas X SMK

Summary

This video provides a detailed introduction to trigonometric ratios in right-angled triangles. It explains key concepts like sine, cosine, and tangent, and their relationships with the sides of the triangle. Through clear examples, the video demonstrates how to apply these ratios to calculate missing side lengths using the Pythagorean theorem. The script also offers practical tips for remembering the formulas and includes exercises to reinforce understanding. Ideal for beginners, it ensures a strong foundation in trigonometry with easy-to-follow explanations.

Takeaways

• 😀 A right-angled triangle has one angle of 90 degrees.
• 😀 In a right-angled triangle, the sides are named based on their positions relative to the angles: opposite, adjacent, and hypotenuse.
• 😀 The hypotenuse is the longest side and is opposite the right angle.
• 😀 The side opposite the reference angle is called the opposite side, and the side adjacent to the reference angle is the adjacent side.
• 😀 The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
• 😀 Sin of an angle is calculated as the ratio of the opposite side to the hypotenuse.
• 😀 Cos of an angle is calculated as the ratio of the adjacent side to the hypotenuse.
• 😀 Tan of an angle is calculated as the ratio of the opposite side to the adjacent side.
• 😀 A mnemonic to remember the trigonometric ratios is 'Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent'.
• 😀 When solving for missing sides in a right-angled triangle, the Pythagorean theorem can be used to find the third side if two sides are known.

Q & A

What is a right triangle?

A right triangle is a triangle where one of the angles is a right angle, meaning it measures 90 degrees.

What is the hypotenuse in a right triangle?

The hypotenuse is the side opposite the right angle, and it is the longest side of the triangle.

What are the three main trigonometric ratios used in right triangles?

The three main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

How is sine (sin) defined in terms of the sides of a right triangle?

Sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Formula: sin(α) = Opposite / Hypotenuse.

How is cosine (cos) defined in terms of the sides of a right triangle?

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(α) = Adjacent / Hypotenuse.

What does tangent (tan) represent in a right triangle?

Tangent (tan) of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side. Formula: tan(α) = Opposite / Adjacent.

How can the Pythagorean theorem be used in trigonometry?

The Pythagorean theorem relates the sides of a right triangle: a² + b² = c², where 'a' and 'b' are the legs, and 'c' is the hypotenuse. It helps in finding missing side lengths when two sides are known.

What is the formula for sin(α) in the example given with triangle ABC?

In triangle ABC, where angle α is the reference angle, sin(α) = Opposite / Hypotenuse = BC / AC.

How can we calculate the missing side in a right triangle using trigonometry?

If you know two sides of a right triangle, you can use trigonometric ratios to calculate the third side. For example, use the sine, cosine, or tangent formulas based on the known sides and angles.

What is the reciprocal of sine, cosine, and tangent, and what are their names?

The reciprocals of sine, cosine, and tangent are cosecant (csc), secant (sec), and cotangent (cot), respectively. These are used to calculate the reciprocal values of the trigonometric ratios.