Processing Math: Done

From Förberedande kurs i matematik 1

The idea is first to find the general solution to the equation and then to see which angles lie between 0 and 360.

If we start by considering the expression 2v+10 as an unknown, then we have a usual basic trigonometric equation. One solution which we can see directly is

2v+10=110

There is then a further solution which satisfies 02v+10360, where 2v+10 lies in the third quadrant and makes the same angle with the negative y-axis as 100 makes with the positive y -axis, i.e. 2v+10 makes an angle 110−90=20  with the negative y -axis and consequently

2v+10=270−20=250

There is then a further solution which satisfies 02v+10360, where 2v+10 lies in the third quadrant and makes the same angle with the negative y-axis as 100 makes with the positive y -axis, i.e. 2v+10 makes an angle 110−90=20  with the negative y -axis and consequently

2v+10=270−20=250

FIGURE1 FIGURE2

Now it is easy to write down the general solution,

2v+10=110+n360 and

2v+10=250+n360

and if we make v the subject, we get

v=50+n180 and

v=120+n180 EQ6

For different values of the integers n, we see that the corresponding solutions are:

n=−2n=−1n=0n=1n=2n=3v=50−2180=−310v=50−1180=−130v=50+0180=50v=50+1180=230v=50+2180=410v=50+3180=590v=120−2180=−240v=120−1180=−60v=120+0180=120v=120+1180=300v=120+2180=480v=120+3180=660

From the table, we see that the solutions that are between 0 and 360 are

v=50v=120v=230 and v=300