Question

Sin(2θ)=1/2?

Answer 1

`color(green)(theta=pi/12` or `color(green)((11pi)/12`, `theta = color(brown)(15^@` or `color(brown)(165^@`

Generalized form is
`theta =2kpi + pi/12` or `2k pi + (11pi)/12` for `k` `epsilon` `ZZ`

Explanation:

From the table, we can deduct that:

`sin(pi/6)=1/2`

∴ `2theta=pi/6` or `pi - (pi)/6 = (5pi)/6` or `30^@` or (180 - 30 = 150^@# as sin is positive in I & II quadrants.

∴ `color(green)(theta=pi/12` or `color(green)((11pi)/12`, `theta = color(brown)(15^@` or `color(brown)(165^@`

Since sin is a continuous repetitive function, we can generalize as

`theta =2kpi + pi/12` or `2k pi + (11pi)/12` for `k` `epsilon` `ZZ`

Answer 2

`t = pi/12 + kpi`
`t = (5pi)/12 + kpi`

Explanation:

`sin 2t = 1/2`
Trig table and unit circle give 2 solutions:
a. `2t = pi/6 + 2kpi`-->
`t = pi/12 + kpi`
b. `2t = (5pi)/6 + 2kpi` -->
`t = (5pi)/12 + kpi`