1. The problem is to solve the equation $$\sin(0.5t) + 0.3t = 1$$ for the variable $t$. 2. This is a transcendental equation because it involves both a trigonometric function and a linear term in $t$. 3. There is no simple algebraic formula to isolate $t$ here, so we use numerical methods or graphical analysis to find approximate solutions. 4. Let's analyze the behavior: - The sine function $\sin(0.5t)$ oscillates between $-1$ and $1$. - The term $0.3t$ grows linearly. 5. We want to find $t$ such that the sum equals 1. 6. By testing some values: - At $t=0$, $\sin(0) + 0 = 0$ (less than 1). - At $t=2$, $\sin(1) + 0.6 \approx 0.84 + 0.6 = 1.44$ (greater than 1). 7. So a root exists between $t=0$ and $t=2$. 8. Using a numerical solver (e.g., Newton-Raphson or bisection), the approximate solution is: $$t \approx 1.2$$ 9. This is the value of $t$ that satisfies the equation within reasonable approximation. Final answer: $$t \approx 1.2$$