TRIGONOMETRY A4

If Sin8x = 0.9848 and 0⁰ ≤ x ≤ 360⁰, solve for x.

Solution

Sin8x = 0.9848 ………….. (i)

Sin80⁰= 0.9848 ………….. (ii)

equating (i) and (ii),

8x = 80⁰

8x = 80⁰

8      8

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 – 80⁰) = Sin100⁰

Then,

Sin8x = 0.5 ………….. (i)

Sin100⁰= 0.5………….. (iii)

Equating (i) and (iii),

8x = 100⁰

8x = 100⁰

8       8

x = 12.5⁰

Hence x = 10⁰ or x = 12.5⁰ answer

TRY THIS………….

If Sin2x = 0.9397 and 0⁰ ≤ x ≤ 360⁰, solve for x.