TRIGONOMETRY D1

If Sin15x = 0.5 and 0⁰ ≤ x ≤ 360⁰, solve for x.

Solution

Sin15x = 0.5 ………….. (i)

Sin30⁰= 0.5………….. (ii)

equating (i) and (ii),

15x = 30⁰

15x = 30⁰

15      15

x = 2⁰

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= 10⁰

In the 2nd quadrant,

SinӨ= Sin(180⁰ – Ө)

Sin30⁰= Sin(180⁰ – 30⁰) = Sin150⁰

Then,

Sin15x = 0.5 ………….. (i)

Sin150⁰= 0.5………….. (iii)

Equating (i) and (iii),

15x = 150⁰

15x = 150⁰

15       15

x = 10⁰

Hence x = 2⁰ or x = 10⁰ answer

TRY THIS…………

If Sin(2x-10) = 0.8 and 0⁰ ≤ x ≤ 360⁰, solve for x.