Question

Solve arcsin √13t with steps:

a. sin-1(√13t) = θ
b. 13t = sin²(θ)
c. t = sin²(θ)/13
d. Other
⁡

Answer 1

To solve for t in the equation arcsin(√13t), you need to set this equation equal to θ, square both sides to get rid of the square root, giving sin²(θ) = 13t, and then divide both sides by 13 to get t = sin²(θ) / 13.

Step-by-step explanation:

The question involves solving for the variable t in the equation given by the arcsine function, also denoted as sin-1. Here's how you solve sin-1(√13t):

1. Let θ be the angle whose sine is √13t, so sin-1(√13t) = θ.
2. Since sin(θ) = √13t, we square both sides to get rid of the square root, resulting in sin2(θ) = 13t.
3. Divide both sides by 13 to solve for t, which gives us t = sin2(θ) / 13.
4. Therefore, t = sin2(θ) / 13 is our final expression for t.

It's important to note that this solution only works when θ is in the domain of the arcsine function, which is [-π/2, π/2], and √13t must be between -1 and 1.