find the range of
sin(siny)+cos(siny)
To find the range of the function f(x) = sin(siny) + cos(siny), we need to determine the possible values that this function can take. Here's how you can solve it step by step:
Step 1: Identify the domain of the function.
Since the function involves sin(siny) and cos(siny), we need to determine the domain of siny. The domain of the sine and cosine functions is all real numbers, so siny can take any value in the interval (-∞, ∞).
Step 2: Evaluate the minimum and maximum values of the function.
To determine the minimum and maximum values, we can analyze the behavior of sin(siny) and cos(siny).
The range of the sine function is [-1, 1]. Therefore, sin(siny) can take any value between -1 and 1.
The range of the cosine function is also [-1, 1]. Hence, cos(siny) can also take any value between -1 and 1.
Since f(x) = sin(siny) + cos(siny), the sum of two values that are each between -1 and 1 will always be between -2 and 2.
Step 3: Determine the range of the function.
Combining everything together, we can conclude that the range of the function f(x) = sin(siny) + cos(siny) is [-2, 2].
So, the range of the given function is [-2, 2].