How many solution exist for $\sin(x^e)/\cos(x) - 2 = 0$?

Question

Here I am trying to find how many solutions exist for the equation in the range $(0,\pi/2)$. $\sin(x^e)/\cos(x) - 2 = 0$

Solving it through the graph is easy so shall I draw the graph of $\sin(x^e)$ and $\cos (x)$ and compare those two? or I need to include some other thing as well in the graph?

What can be my matlab code to solve this equation ? Can I solve it using

x = 0:0.01: pi/2;
y = sin(x^e);
z = cos(x);
plot(x,y,x,z)

How to include $-2$ in this code?

Answer 1

In[5]:= Plot[f[x], {x, 0, Pi/2}, Ticks -> {{Pi/6, Pi/3, Pi/2}, Automatic}] Plot the graph and see that there are two zeros: One around 1.07974 and one around 1.49678. Use Newtons method to get as many digits as you desire, e. g. 30: x=N[11/10,30]; For[n = 1, n <= 6, n++, Print[N[x, 30]]; x = x - f[x]/f'[x]] This will deliver 1.0797390735632027377559062453. The same with initial value x=N[15/10,30]: This will deliver 1.4967796651840889289769323. Hope this is precise enough for you.