TRIGONOMETRY 1

If Sin6x = 0.5 and 0⁰ ≤ x ≤ 360⁰, solve for x.

Solution

Sin6x = 0.5 ………….. (i)

Sin30⁰= 0.5………….. (ii)

equating (i) and (ii),

6x = 30⁰

6x = 30⁰

6      6

x = 5⁰

From the given question we see that sine is positive.

From the range of 0⁰ up to 360⁰ sine is positive in the 1st and 2nd quadrants.

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

In the 1st quadrant,

x= 5⁰

In the 2nd quadrant,

SinӨ= Sin(180⁰ – Ө)

Sin30⁰= Sin(180⁰ – 30⁰) = Sin150⁰

        Then,

Sin6x = 0.5 ………….. (i)

Sin150⁰= 0.5………….. (iii)

Equating (i) and (iii),

6x = 150⁰

6x = 150⁰

6       6

x = 25⁰

Hence x = 5⁰ or x = 25⁰ answer

TRY THIS…………

If Sin(2x-10) = 0.5 and 0⁰ ≤ x ≤ 360⁰, solve for x.