Question

Draw the graph of y = sin -¹x (or any other inverse
trigonometric function), using the graph of
y = sin x (or any other relevant trigonometric
function). Demonstrate the concept of mirror line
(about y = x) and find its domain and range..​

Answer 1

Answer:

Step-by-step explanation:

Consider, y = sin-1x + cos-1x

y = sin-1x + cos-1x; x ∈ [−1,1]

y = π/2

Therefore, graphical representation of y = sin-1x + cos-1x is y =π/2 for x∈[−1,1] is given below:

Answer 2

Draw the graph of y = sin -¹x using the graph of y = sinx. Demonstrate the concept of mirror line (about y = x) and find it domain and range.

before going to solve this question, we should know something about inverse function.

inverse function is bijective function, means it is one - one and onto function.

but sinx is a many-one function after all, it cut more than one time a straight line drawn parallel to x - axis.

so we have to choose a specific range of sinx and then find its inverse. this way, we can do inverse of any trigonometric function.

so let's take y = sinx in the range of [ -π/2, π/2]

we know, if y = f(x) is a function, then x = f¯¹(y) is inverse of it and it is mirror image of y = f(x) about y = x.

from this concept, we can draw y = sin¯¹x graph,

see diagram, it is clearly demonstrated the concept of mirror line about y = x.

now from graph, it is also clear that domain of y = sin¯¹x is [-1, 1] and range is [π/2, -π/2]