In a magical mathematical kingdom, there are three mathematical heroes, namely Mr Sine, Mr Cosine and Mr Tangent. They all like to explore the mysteries of trigonometric functions very much.
One day, Mr. Sinny decided to explore the nearby mountains. He found a high mountain and wanted to know its height. Mr Sine is considering how to measure the height of the mountain peak. Suddenly, Mr. Sinny came over.
Mr. Cosine told Mr. Sine that he could calculate the height of the mountain by measuring the distance between himself and Mr. Tangent and the observed angle. So they found Mr. Tangent standing at the foot of the mountain.
Mr. Sine measures the distance between himself and Mr. Tangent, and records it as A, and then observes the angle of direct sunlight, and records it as θ. Mr. Cosine told him that according to the basic relationship of trigonometric function, the height of mountain peak can be calculated by tangent function.
Mr Sine was curious about this, so they made a calculation together. According to the definition of the tangent function, the tangent θ is equal to the ratio of the opposite side (the height of the mountain peak) to the adjacent side (the distance a). So, Mr Sine calculated the height of the mountain with the measured distance A and the observed angle θ.
This story tells us that there is a basic relationship between trigonometric functions with the same angle. Sine function represents the ratio of opposite side to hypotenuse, cosine function represents the ratio of adjacent side to hypotenuse, and tangent function represents the ratio of opposite side to adjacent side. Using the relationship of these functions, we can deduce the values of other unknown quantities when one quantity is known.
I hope this digital story can help you understand the basic relationship between trigonometric functions and angles. If you have any other questions, I will try my best to answer them for you.
Trigonometric function with the same angle means that there is a specific mathematical relationship between different trigonometric functions for the same angle. It mainly includes sine, cosine and tangent functions.
1. Sinusoidal function: Sinusoidal function indicates the ratio of the opposite side to the hypotenuse of an angle, usually expressed by sine. For a triangle with an angle θ, the sine function can be expressed as sin(θ)= opposite side/hypotenuse.
2. Cosine function: Cosine function represents the ratio of the adjacent side to the hypotenuse of an angle, usually expressed by cos. For a triangle with an angle θ, the cosine function can be expressed as cos(θ)= adjacent side/hypotenuse.
3. Tangent function: Tangent function represents the ratio of the opposite side to the adjacent side of an angle, usually expressed by Tan. For a triangle with angle θ, the tangent function can be expressed as tan(θ)= opposite side/adjacent side.