Paul's Online Notes
Home / Calculus I / Derivatives / Derivatives of Trig Functions
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 3-5 : Derivatives of Trig Functions

For problems 1 – 3 evaluate the given limit.

1. $$\displaystyle \mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{z}$$ Solution
2. $$\displaystyle \mathop {\lim }\limits_{\alpha \to \,0} \frac{{\sin \left( {12\alpha } \right)}}{{\sin \left( {5\alpha } \right)}}$$ Solution
3. $$\displaystyle \mathop {\lim }\limits_{x \to \,0} \frac{{\cos \left( {4x} \right) - 1}}{x}$$ Solution

For problems 4 – 10 differentiate the given function.

1. $$f\left( x \right) = 2\cos \left( x \right) - 6\sec \left( x \right) + 3$$ Solution
2. $$g\left( z \right) = 10\tan \left( z \right) - 2\cot \left( z \right)$$ Solution
3. $$f\left( w \right) = \tan \left( w \right)\sec \left( w \right)$$ Solution
4. $$h\left( t \right) = {t^3} - {t^2}\sin \left( t \right)$$ Solution
5. $$y = 6 + 4\sqrt x \,\csc \left( x \right)$$ Solution
6. $$\displaystyle R\left( t \right) = \frac{1}{{2\sin \left( t \right) - 4\cos \left( t \right)}}$$ Solution
7. $$\displaystyle Z\left( v \right) = \frac{{v + \tan \left( v \right)}}{{1 + \csc \left( v \right)}}$$ Solution
8. Find the tangent line to $$f\left( x \right) = \tan \left( x \right) + 9\cos \left( x \right)$$ at $$x = \pi$$. Solution
9. The position of an object is given by $$s\left( t \right) = 2 + 7\cos \left( t \right)$$ determine all the points where the object is not moving. Solution
10. Where in the range $$\left[ { - 2,7} \right]$$ is the function $$f\left( x \right) = 4\cos \left( x \right) - x$$ is increasing and decreasing. Solution