Vektor Fisika • Part 1: Pengantar Trigonometri Dasar

Summary

In this educational video, Christian Sutantio explains the basics of trigonometry for high school physics students, specifically focusing on vectors. He introduces key trigonometric functions—sine, cosine, and tangent—and their relationships to angles and sides of right-angled triangles. Special angles and their sine, cosine, and tangent values are discussed, along with how to calculate these functions for angles greater than 90°, considering their quadrant positions. The video includes practical examples to reinforce the application of these concepts in solving vector problems, encouraging students to practice and apply the material for a deeper understanding.

Takeaways

• 😀 Trigonometry is the branch of mathematics that deals with angles and triangles, specifically focusing on sine, cosine, and tangent functions.
• 😀 The sine (sin), cosine (cos), and tangent (tan) are the three primary trigonometric functions used to solve vector problems in physics.
• 😀 In a right triangle, the side opposite the angle is referred to as the 'opposite' side, the adjacent side as the 'adjacent' side, and the hypotenuse as the 'hypotenuse'.
• 😀 Sin(Alpha) = opposite/hypotenuse, Cos(Alpha) = adjacent/hypotenuse, and Tan(Alpha) = opposite/adjacent.
• 😀 Special angles such as 0°, 30°, 45°, 60°, and 90° have fixed values for sin, cos, and tan, which must be memorized.
• 😀 A simple mnemonic to remember these functions for angles is 'Sin Demi Kau Tami Fan Besok' – representing the relationships between sin, cos, and tan.
• 😀 When dealing with angles over 90°, the signs of the trigonometric functions change depending on the quadrant of the angle.
• 😀 The four quadrants (1st, 2nd, 3rd, and 4th) follow specific rules for the signs of sin, cos, and tan: all positive in the 1st quadrant, only sin positive in the 2nd, only tan positive in the 3rd, and only cos positive in the 4th.
• 😀 For angles over 180° but less than 360°, we apply trigonometric identities such as Sin(180° - Alpha) = Sin(Alpha) and Cos(180° + Alpha) = -Cos(Alpha).
• 😀 Practical examples for calculating sin, cos, and tan of angles over 90° or within different quadrants are shown with real-world applications in physics, particularly in vector problems.

Q & A

What is trigonometry and why is it important in understanding vectors?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is important in understanding vectors because it helps in breaking down vector components and performing calculations like dot products and cross products using sine, cosine, and tangent functions.

What are the six trigonometric functions?

There are six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). In the video, only the first three functions—sine, cosine, and tangent—are discussed.

How is sine (sin) defined and calculated?

Sine (sin) of an angle is defined as the ratio of the side opposite the angle to the hypotenuse of the triangle. Mathematically, it is written as sin(α) = opposite / hypotenuse.

What is the relationship between cosine (cos) and sine (sin)?

Cosine (cos) is the ratio of the adjacent side to the hypotenuse. Cosine is often thought of as the complement of sine, meaning that cos(α) = sin(90° - α), and vice versa.

How can tangent (tan) be calculated?

Tangent (tan) of an angle is the ratio of the side opposite the angle to the side adjacent to the angle. Mathematically, tan(α) = opposite / adjacent.

How can one memorize the values of sine, cosine, and tangent for special angles like 0°, 30°, 45°, 60°, and 90°?

For special angles, the values of sine, cosine, and tangent can be memorized using a specific pattern. For sine, the values are 0, 1/2, √2/2, √3/2, and 1. Cosine has the same values but in reverse order, and tangent follows a simple sequence like 0, 1/√3, 1, √3, and undefined.

What is the significance of the four quadrants in the unit circle for trigonometry?

The unit circle is divided into four quadrants. The signs of sine, cosine, and tangent differ across these quadrants. In Quadrant I, all functions are positive. In Quadrant II, sine is positive, but cosine and tangent are negative. In Quadrant III, tangent is positive, while sine and cosine are negative. In Quadrant IV, cosine is positive, but sine and tangent are negative.

What formula can be used to find the values of sine, cosine, or tangent for angles greater than 90°?

To find the values of trigonometric functions for angles greater than 90°, you can use the angle's reference angle and determine the sign based on the quadrant. For example, sin(120°) can be found by using sin(180° - 60°) and adjusting the sign for Quadrant II, where sine is positive.

How do you calculate the trigonometric functions for an angle in the third quadrant, such as 225°?

For angles in the third quadrant, you can use the formula sin(180° + α), cos(180° + α), or tan(180° + α). The reference angle is the difference from 180°. The signs of sine and cosine will be negative, but tangent will be positive in this quadrant.

What is the formula for determining the sine or cosine of an angle when it's between 180° and 270°?

For angles between 180° and 270° (Quadrant III), you use the formula sin(180° + α) or cos(180° + α). The sine and cosine will be negative, but tangent will be positive in this quadrant.