Repeats every 360o

1
Y Sin q
Repeats every 360o
2 solutions every 360o
2
Y Cos q
Repeats every 360o
2 solutions every 360o
3
Y Tan q
Repeats every 180o
1 solution every 180o
4
All
Sin
Tan
Cos
5
Y Sin 3q
There are 6 solutions except for when sin 3q 1
or -1
6
Cos 3q 0.5602
For 0o ? q ? 360o
3q 55.9o and 360 - 55.9o
3q 55.9o and 304.1o
But what about second time round or third?
so 3q 55.9o and 304.1o or 55.9360o and
304.1360o or 55.9720o and 304.1720o
so 3q 55.9o and 304.1o or 415.9o and 664.1o
or 775.9o
and 1024.1o
q 18.6o, 101.4o, 138.6o, 221.4o, 258.6o, 341.4o
7
Sin (3q-25o) 0.234
For 0o ? q ? 360o
3q-25o 13.5o and 180 - 13.5o
3q-25o 13.5o and 166.5o
But what about second time round or third?
so 3q-25o 13.5o and 166.5o or 13.5360o and
166.5360o or 13.5720o and 166.5720o
3q-25 13.5o and 166.5o or 373.5o and
526.5o or 733.5o and 886.5o
3q 38.5o, 191.5o, 398.5o, 551.5o, 758.5o, 911.5o
q 12.8o, 63.8o, 132.8o, 183.8o, 252.8o, 308.8o
8
Sin (3q25o) 0.234
For 0o ? q ? 360o
so 3q25o 13.5o,166.5o, or 13.5 360o,
166.5 360o, 13.5 720o, 166.5 720o
3q -11.5o and 168.5o or 348.5o and
528.5o or 708.5o and 888.5o
But one of the answers is negative so find the
next solution going round a fourth time
3q -11.5 1080o 1068.5
3q 168.5o, 348.5o, 528.5o, 708.5o, 888.5o,
1068.5o
q 56.2o, 116.2o, 176.2o, 236.2o, 296.2o, 356.2o