To find cos(x) and tan(x) given that sin(x) = 12, we first need to recognize an important fact about the sine function. The value of sine, sin(x), must always fall within the range of -1 to 1 for real numbers. Therefore, sin(x) = 12 is not possible in the context of real angles.
Since sin(x) is greater than 1, it indicates that either the angle x is not a real angle or we are dealing with an extended or complex scenario which doesn’t adhere to the basic properties of trigonometric functions.
As a result, we cannot compute cos(x) or tan(x) based on the value of sin(x) = 12 since it is outside the valid range for the sine function.
In summary, it is essential to ensure that the values of trigonometric functions are within their standard limits before attempting to calculate other trigonometric ratios. Since sin(x) cannot be 12, we conclude that cos(x) and tan(x) cannot be determined in this case.