Maths and Vibrations Tutorial Sheet 2

Maths and Vibrations Tutorial Sheet 2

1) Sketch the functions sin(x), cos(x) and tan(x) and also cosec(x), sec(x) and cot(x) between -p and p. Note the angles where they cross the axes and indicate any asymptotes. Which are odd or even functions ?

2) Sketch |sin(x)| and sin²(x) between -p and p

3) Sketch 2cos(x) and cos 2x) between -p and p

4) Solve the following equations for q between 0 and 360^o,

i ii)

5) Show

i) Clue you will need to factorise a polynomial.

ii) Clue look at factor formulae.

Give the coordinates where the following lines cross the axes,

i ii)

7) Find the distance between the points (0,7) and (12,-2) and the equation of the line joining the points.

Indicate which variables could be plotted in order to obtain a straight line graph from x, y data,

i ii) iii)