the graph of an inverse trigonometric function passes through the point (1,pi/2). which of the following could be the equation of the function
Y=Cos^-1 x
Y=cot^-1 x
Y=Sin^-1 x
Y=Tan^-1 x
which of the functions is 1 at π/2?
Yes
To determine which equation represents the inverse trigonometric function, let's analyze the given information. We are given that the graph passes through the point (1, π/2).
The inverse trigonometric function will have a range restricted to a specific interval depending on the trigonometric function.
Let's analyze each equation:
1. Y = Cos^(-1)x: The range of the inverse cosine function is [0, π]. Therefore, the point (1, π/2) does not lie on this graph as π/2 is not in the range of arccosine.
2. Y = Cot^(-1)x: The range of the inverse cotangent function is (0, π). Therefore, the point (1, π/2) does not lie on this graph as π/2 is outside the range of arccotangent.
3. Y = Sin^(-1)x: The range of the inverse sine function is [-π/2, π/2]. Therefore, the point (1, π/2) lies on this graph as π/2 is in the range of arcsine.
4. Y = Tan^(-1)x: The range of the inverse tangent function is (-π/2, π/2). Therefore, the point (1, π/2) does not lie on this graph as π/2 is outside the range of arctangent.
Based on the given point (1, π/2), the equation that could represent the function is Y = Sin^(-1)x.
Remember, when you are unsure about the graph of inverse trigonometric functions, it is helpful to consider the range of each function to determine which equation is appropriate.