period of cos x

apparently this question has nothing to do with what i asked you only need to know that cos^-1(0) is 90 and 270 to find the value o beta but the problem is if you only write 90 and forget about 270 will you lose mark for it?

apparently this question has nothing to do with what i asked you only need to know that cos^-1(0) is 90 and 270 to find the value o beta but the problem is if you only write 90 and forget about 270 will you lose mark for it?

apparently this question has nothing to do with what i asked you only need to know that cos^-1(0) is 90 and 270 to find the value o beta but the problem is if you only write 90 and forget about 270 will you lose mark for it?

am i too late?

You will. For cosine, besides for the inverse cosine solution, x, there is the solution 360 - x, and then each of these solution generates more with period 360. You'll have to give all the solutions in the range given.

You are missing a solution if you don't find the value of theta that gives you 7theta/6 = 270 so you will lose some marks for it.

In general, you have to look at the range that theta can take and then look for x values such that cosx = .. whatever you're looking for.

Eg if you're looking for values of theta in the range 0 to 180 degrees such that cos2theta = 0, then you need to look for x values (where x = 2theta) between 0 and 360.

seems like i should memorise all the values of cos, sin and tan for example in the picture i attached you here how am i supposed to know that cos of all these values will give -1/2 ?memorising is the only way or am i missing something?

You will. For cosine, besides for the inverse cosine solution, x, there is the solution 360 - x, and then each of these solution generates more with period 360. You'll have to give all the solutions in the range given.

so basically the periodic of sin and cos is 360?

You can use a calculator to find one value, then use a CAST diagram or the graphs to find the other values.

Yes, sine and cosine are periodic functions with period 360 degrees.

Tangent has a period of 180 degrees.

found the first value of x using calculator to be 2pi/15 , according to cast diagram i only need to subtract pi from the angle i just found to get the next one between the interval of the question which is 0<x<pi but there are like 5 angles
here's the full question it's in the factor formula chapter btw

What range of x values do you think you should be looking for?

between zero and pi?

0<x<pi -> 0<5x<5pi, so you need to look for angles with a cos of -1/2 between 0 and 5pi.
You found 2pi/3, so another solution is 2pi-2pi/3=4pi/3. Now keep adding 2pi onto each of these two solutions to get more solutions, until you go above 5pi.