The Origins of Sine, Cosine, and Tangent: Explained

🔑Sine, cosine, and tangent are commonly found as buttons on scientific calculators and are essential in mathematics.

🎯The value of pi, obtained by dividing a circle's circumference by its diameter, plays a significant role in trigonometry.

🧩Right angle triangles with a 60-degree angle always have the opposite side divided by the hypotenuse equal to 0.866.

🔍Similar to sine, cosine can be calculated by dividing the adjacent side by the hypotenuse in right angle triangles.

🌈The values of sine, cosine, and tangent form a curve known as the sine wave, which has various applications in maths and science.

Where do sine, cosine, and tangent come from?

—Sine, cosine, and tangent are derived from the relationship between angles and sides in right angle triangles.

What is the importance of pi in trigonometry?

—Pi, obtained by dividing a circle's circumference by its diameter, is crucial in calculations involving angles in trigonometry.

How are sine, cosine, and tangent calculated?

—Sine is calculated by dividing the length of the side opposite the angle by the length of the hypotenuse in a right angle triangle. Cosine is calculated by dividing the length of the side adjacent to the angle by the length of the hypotenuse. Tangent is calculated by dividing the length of the side opposite the angle by the length of the side adjacent to the angle.

Do sine, cosine, and tangent have applications beyond trigonometry?

—Yes, the values of sine, cosine, and tangent are used in various fields such as physics, engineering, and computer graphics to model and calculate patterns, waves, and rotations.

What is the relationship between sine, cosine, and tangent?

—Sine and cosine are fundamental trigonometric functions, while tangent is derived from dividing sine by cosine. They are all interrelated and play key roles in solving trigonometric equations and problems.

00:01Sine, cosine, and tangent are commonly found on scientific calculators and are essential in mathematics.

01:22The value of pi, obtained by dividing a circle's circumference by its diameter, plays a significant role in trigonometry.

03:08Right angle triangles with a 60-degree angle always have the opposite side divided by the hypotenuse equal to 0.866.

07:40Similar to sine, cosine can be calculated by dividing the adjacent side by the hypotenuse in right angle triangles.

08:22The values of sine, cosine, and tangent form a curve known as the sine wave, which has various applications in maths and science.