How do I prove this statement?
sin^-1(sin Ø) = Ø
I can't figure out how I would go about proving it. Any help is appreciated.
Isn't it proved by definition?
The angle whose sine is the sine of theta, is theta.
is proven by reflexive property .
P.S. this is not algebra its trigonometry
To prove the statement sin^(-1)(sin Ø) = Ø, you need to use the properties of the inverse sine function and the sine function itself. Here's a step-by-step guide on how to prove it:
1. Start with the left-hand side of the equation: sin^(-1)(sin Ø).
2. Recall that sin^(-1) represents the inverse sine function, also known as arcsin, which is the function that undoes the sine function.
3. Consider the property of the inverse sine function: it returns an angle between -π/2 and π/2.
4. Now, think about the relationship between the sine function and the inverse sine function. The sine function takes an angle as an input and produces a corresponding value between -1 and 1.
5. As a result, sin^(-1)(sin Ø) will return an angle within the interval of -π/2 and π/2.
6. On the right-hand side of the equation, Ø represents an angle.
7. Given that Ø is an angle within the interval of -π/2 and π/2, it satisfies the conditions of the inverse sine function.
8. Therefore, sin^(-1)(sin Ø) = Ø, as both sides of the equation represent an angle within the range -π/2 to π/2.
By reasoning through the properties of the inverse sine function and the sine function, you can prove that sin^(-1)(sin Ø) = Ø.