TRIGONOMETRY A1

If Sin3x = 0.5 and 0⁰ ≤ x ≤ 360⁰, solve for x.

solution

Sin3x = 0.5 ………….. (i)

Sin30⁰= 0.5………….. (ii)

equating (i) and (ii),

3x = 30⁰

3x = 30⁰

3      3

x = 10⁰

From the given question we see that sine is positive.

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

In the 1st quadrant,

x= 10⁰

In the 2nd quadrant,

SinӨ= Sin(180⁰ – Ө)

Sin30⁰= Sin(180⁰ – 30⁰) = Sin150⁰

Then,

Sin3x = 0.5 ………….. (i)

Sin150⁰= 0.5………….. (iii)

Equating (i) and (iii),

3x = 150⁰

3x = 150⁰

3       3

x = 50⁰

Hence x = 50⁰ or x = 10⁰ answer

TRY THIS………….

If Sin2x = 0.8 and 0⁰ ≤ x ≤ 360⁰, solve for x.