Sin(t)
Definition
The sine function, denoted as sin(t), is a mathematical function that relates the angle t of a right triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Analogy
Imagine you are on a Ferris wheel and your seat is at its highest point. As you go down, your height decreases until you reach the lowest point. The height variation can be represented by the sine function.
Related terms
Cos(t): The cosine function, denoted as cos(t), is another trigonometric function that relates an angle t to the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Tan(t): The tangent function, denoted as tan(t), is a trigonometric function that represents the ratio between sin(t) and cos(t). It relates an angle t to the ratio of sin(t) divided by cos(t).
Periodicity: In trigonometry, periodicity refers to how certain functions repeat their values after specific intervals. For example, sin(t) has a period of 2π radians or 360 degrees, meaning it repeats its values every 2π radians or 360 degrees.
"Sin(t)" appears in:
Study guides (1)
Practice Questions (3)
A particle moves along a straight line, and its position function is given by x(t) = sin(t). At which of the following times is the particle momentarily at rest?
If the position function of a particle is given by s(t) = 5sin(t) + 2cos(t), what is the velocity of the particle at t = π/4?
A particle moves on the xy-plane. Its motion can be described by the parametric functions y(t) = sin(t) and x(t) = cos(t). What will the path of the particle look like?
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