Consider the following parametric curve: y = tan(t), where 0 < t < π/2. Find the first derivative dy in general. Simplify your answer completely and express it in terms of sin(t) and cos(t) only. No double fractions in the final answer.
Consider the following parametric curve: x = t, y = 5t - 7, where -π/2 < t < π/2. Find the second derivative d²y/dx² in general. Simplify your answer completely. No double fractions in the final answer. No negative powers in the final answer. Convert fractional powers to roots in the final answer.
Write an equation of the tangent line to the curve at the point where t = 8. Simplify the final answer and write it as something like y = mx + b.