whats the domain and range of sine and tan?
The sine ranges from -1 to +1. Its domain is all postive and negative numbers.
I will be happy to critique your thinking on tangent.
The tangent function, denoted as tan(x), has a different domain and range compared to the sine function.
The domain of the tangent function is all real numbers, except for the values where the cosine function (denoted as cos(x)) equals zero. Cosine is the denominator of the tangent function, so when cosine is zero, the tangent function becomes undefined. In other words, the domain of tan(x) is all real numbers except for the values of x where cos(x) = 0.
To find the values of x where cos(x) = 0, you can use the unit circle or the graph of the cosine function. The cosine function equals zero when x is equal to odd multiples of π/2. So, the values to exclude from the domain of tan(x) are x = π/2, 3π/2, 5π/2, and so on.
The range of the tangent function is all real numbers, excluding values where the function goes to infinity or negative infinity. The tangent function is periodic with a period of π, which means it repeats itself every π units. As x approaches these points, the tangent function approaches positive or negative infinity.
To summarize:
- The domain of the tangent function tan(x) is all real numbers except for odd multiples of π/2.
- The range of the tangent function tan(x) is all real numbers excluding points where it goes to infinity or negative infinity.