Thread: Finding solutions within the range?

Hi folks,new to the forum and would like to start by asking for help in four trignometry questions,lol!

As the title says, I have to find all solutions within the given range, Ive been racking my brains all day and can't get anywhere. They are as follows:

8.2 tan 2x = 10 0< x <180


5 cos 8 ( θ - 16) = -13 0 < θ < 140



5 sin 6x = -2 0< x < π



50 sin (3 θ + π/6) = 30 0< θ <2.5

π = pi (it doesnt appear to be clear the way ive written it

any help would be highly appreciated.

Thanks.

well you do the first one like this:

8.2 tan 2x = 10 0< x <180

divide the 8.2 to the other side
tan 2x = 10/8.2

take the inverse of tangent which makes it
tan^-1 (10/8.2) = 2x

divide the two so your left with x
and solve with a graphing calculator
[tan^-1 (10/8.2)]/ 2 = x = 25.324

then you can check 8.2*tan(2*25.324) = 9.999999 close enough haha
hope that atleast gets you on the right track

Originally Posted by Tino1210

50 sin (3 θ + π/6) = 30 0< θ <2.5


Thanks.

Divide both sides by 50.



Take arcsin of both sides.





Subtract from both sides and divide by





Check: