TRIGONOMETRY A5

 If Cos 5x = 0.0872 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  = 0.0872………….. (i)

Cos 85⁰ = 0.0872………….. (ii) 

[Because 0.0872 = Cos 85⁰ in mathematical tables.]

Equating (i) and (ii),

5x = 85⁰

5x = 85⁰

5      5

x = 17⁰

In the 4th quadrant,

CosӨ= Cos(360⁰ – Ө)

Cos85⁰= Cos(180⁰ – 85⁰) = Cos95⁰

Then,

Cos5x = 0.0872………….. (i)

Cos95⁰ = 0.0872………….. (iii)

Equating (i) and (iii),

5x = 95⁰

5x = 95⁰

5      5 

 

x = 19⁰

Hence x = 17⁰ or x = 19⁰ answer

TRY THIS………….

If Cos 3y = 0.3090 and 0⁰ ≤ y ≤ 360⁰, solve for y.