TRIGONMETRY A3

If Cos 5x = 0.3420 and 0⁰ ≤ x ≤ 360⁰, solve for x.

Solution

In the range of 0⁰ up to 360⁰ cosine is positive in the 1st and 4th quadrants.

In 1st quadrant,

Cos 5x  = 0.3420 ………….. (i)

Cos 70⁰  = 0.3420 ………….. (ii)

[Because 0.3420 = Cos 70⁰ in mathematical tables.]

Equating (i) and (ii),

5x = 70⁰

5x = 70⁰

5      5

x = 14⁰

In the 4th quadrant,

CosӨ= Cos(360⁰ – Ө)

Cos70⁰= Cos(180⁰ – 70⁰) = Cos110⁰

Then,

Cos5x = 0.3420 ………….. (i)

Cos110⁰ = 0.3420 ………….. (iii)

Equating (i) and (iii),

5x = 110⁰

5x = 110⁰

5       5

x = 22⁰

Hence x = 14⁰ or x = 22⁰ answer

TRY THIS………….

If Cos 3x = 0.4067 and 0⁰ ≤ x ≤ 360⁰, solve for x.