When solving trigonometric problems like finding the inverse sine function, it's important to show your work to demonstrate your understanding of the problem and how you arrived at your answer. Here's an explanation of how you can approach solving sin^-1(4/5) and why it's necessary to show your work.
To find the inverse sine of 4/5, you can use either a calculator or a specific formula. Using a calculator, you can directly input the value 4/5 and find its inverse sine, which would be approximately 0.927295218 radians (or about 53.130102°).
However, if you want to manually solve the problem, it's important to show your work by explaining the steps you took. Here's how you can do it:
1. Recall that sin^-1(x) represents the angle whose sine is x.
2. In this case, you need to find the angle whose sine is 4/5.
3. Write sin^-1(4/5) = θ, where θ is the unknown angle.
4. Rewrite this equation as sin(θ) = 4/5.
5. To find the value of θ, take the inverse sine of both sides: θ = sin^-1(4/5).
6. Use a calculator or a trigonometric table to find the value of sin^-1(4/5), which is approximately 0.927295218 radians.
By showing the steps above, you are demonstrating your understanding of the problem and how you arrived at the answer. It also allows your teacher to see your logical reasoning and approach to solving the problem.
Regarding your question about whether you need to show the formula, it's usually not necessary to write down the specific formula since it is typically implied when solving trigonometric problems. However, if your teacher explicitly requires you to show the formula, it's best to follow their instructions.
If you were my student and you only provided the answer without showing any work, it would be difficult for me to assess your understanding of the problem. I would advise you to communicate with your teacher about the space limitation issue for showing your work. It's possible that they may provide additional space or suggest alternative ways to present your work.