Final answer:
The question involves finding different trigonometric representations for the same graph, including using functions like sine, cosine, and tangent, as well as various trigonometric identities and laws to represent the relationships between triangle sides and angles.
Step-by-step explanation:
The student is asking for various representations of the same graph in trigonometric functions. Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right-angled triangles.
Trigonometric functions such as sine, cosine, and tangent can be used to describe the properties and behavior of waves, oscillations, and circular motion, which are often graphically represented.
Examples of Trigonometric Representations
- Sine Function: sin(θ) is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
- Cosine Function: cos(θ) is the ratio of the adjacent side to the hypotenuse.
- Tangent Function: tan(θ) is the ratio of the opposite side to the adjacent side.
- Variations and Identities: Transformations such as sin(2θ) = 2sin(θ)cos(θ), which show trigonometric functions can be expressed in terms of one another using various identities.
One can also use the law of sines and the law of cosines to relate the sides and angles of any triangle, not just right-angled ones, providing additional ways to represent trigonometric relationships in graphs.
Furthermore, trigonometric functions can be expressed as infinite sums using power series expansions, offering another perspective on these functions.
Your correct question is: What are the key features of trigonometric functions graphs?