–10 –5 5 10

–4

–3

–2

–1

1

2

3

4

x

y

Repeats every 360o

2 solutions every 360o

Y = Sin

–10 –5 5 10

–4

–3

–2

–1

1

2

3

4

x

y

Repeats every 360o

2 solutions every 360o

Y = Cos

–10 –5 5 10

–4

–3

–2

–1

1

2

3

4

x

y

Repeats every 180o

1 solution every 180o

Y = Tan

CosTan

Sin All

2 4 6

–4

–3

–2

–1

1

2

3

4

x

y

Y = Sin 3

There are 6 solutions except for when sin 3 = 1 or -1

Cos 3 = 0.5602

3 = 55.9o and 360 - 55.9o

3 = 55.9o and 304.1o

= 18.6o, 101.4o, 138.6o, 221.4o, 258.6o, 341.4o

But what about second time round or third?

so 3 = 55.9o and 304.1o or 55.9+360o and 304.1+360o or 55.9+720o and 304.1+720o so 3 = 55.9o and 304.1o or 415.9o and 664.1o or 775.9o and 1024.1o

For 0o 360o

Sin (3 = 0.234

3 = 13.5o and 180 - 13.5o

3 = 13.5o and 166.5o

= 12.8o, 63.8o, 132.8o, 183.8o, 252.8o, 308.8o

But what about second time round or third?

so 3 = 13.5o and 166.5o or 13.5+360o and 166.5+360o or 13.5+720o and 166.5+720o 3 = 13.5o and 166.5o or 373.5o and 526.5o or 733.5o and 886.5o

= 38.5o, 191.5o, 398.5o, 551.5o, 758.5o, 911.5o

For 0o 360o

Sin (3 = 0.234

= 56.2o, 116.2o, 176.2o, 236.2o, 296.2o, 356.2o

But one of the answers is negative so find the next solution going round a fourth time

= 168.5o, 348.5o, 528.5o, 708.5o, 888.5o, 1068.5o

3 = -11.5o and 168.5o or 348.5o and 528.5o or 708.5o and 888.5o

3 = -11.5 + 1080o =1068.5

so 3 = 13.5o,166.5o, or 13.5 + 360o, 166.5 + 360o, 13.5 + 720o, 166.5 +720o

For 0o 360o