Solving for h(t) Greater Than 3: Is There a Better Way?

[uchihajeff]

Hi

This is a problem on a practice test.



Function h(t)=ln(1+t) + (3/4)*cos(t/2)

What are the intervals in which h(t) is greater than 3?



So far, the only way I've been able to figure it out is using the "intersect" functionality of my graphing calculator.

Is there a way to isolate the t? Is there a better way to solve this problem, possibly without the calculator?

Thanks
~uchihajeff

 

[HallsofIvy]

Essentially, then, you want to solve the inequality
ln(1+t) + (3/4)*cos(t/2)> 3 which is equivalent to solving the equation
ln(1+t) + (3/4)*cos(t/2)= 3.

Since that involves two different transcendental functions, there is no algebraic way of solving that equation.

 

[uchihajeff]

Thanks for clearing that up. Now I'll go research into what transcendental functions are.