I posted before ;
Write equivalent equations in the form of inverse functions for
a.)x=y+cos theta
b.)cosy=x^2
my answers were
a.)
x= y+ cos theta
cos theta = x-y
theta = cos^-1(x-y)
b.)
cosy=x^2
cos(y) = x^2
y = Cos^-1(x^2)
your post confused me a little. Can you clarify if my answers were wrong.
The confusion arose because the term inverse function has more than one meaning in mathematics. So there was an answer for each interpretation of the term.
However, if you are in the process of studying inverse trigonometric functions, such as arc-sine, arc-cosines, etc, your answers are correct.
Thank you and yes I'm.
Your answers are incorrect. Let's go through the correct steps to write equivalent equations in the form of inverse functions for the given equations.
a) Starting with the equation: x = y + cos(theta)
1. Subtract y from both sides: x - y = cos(theta)
2. To isolate cos(theta), we need to take the inverse cosine of both sides: cos^(-1)(x - y) = theta
So, the correct equivalent equation would be: theta = cos^(-1)(x - y)
b) Starting with the equation: cosy = x^2
1. Apply the inverse cosine to both sides: cos^(-1)(cosy) = cos^(-1)(x^2)
2. Since cos^(-1)(cosy) simplifies to y, we get: y = cos^(-1)(x^2)
So, the correct equivalent equation would be: y = cos^(-1)(x^2)
In summary, the correct forms of the equivalent equations are:
a) theta = cos^(-1)(x - y)
b) y = cos^(-1)(x^2)