change, therefore the value of \(\tan{\theta}\) will change. The graph has a period of 180°. Draw the horizontal line \(y = 0.5\). The line \(y = 0.5\) crosses the graph of \(y = \sin{x}\) ...

Once the tangent is found you can use it to find the gradient of the graph by using the following formula: \(\text{Gradient to the curve =}~\frac {y_2-y_1} {x_2-x_1}\) where \(({x_1,~y_1})\) ...

Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...