find that tan(x) is cos(x)=(1/4). What quadrant is the solution located in.

Question

Trigonometry 

Answer 1

If cos x =1/4 then sec x = 4

 

tanx = ±√(sec²x-1) = ±√([secx]²-1) =±√([4]²-1) = ±√(16-1)=±√15

 

for 0≤x≤π/2, 0≤tanx≤∝ positive

for π≥x≥π/2, x≤∝0≤tanx≤∝ negative

for π≤x≤3π/2, 0≤tanx≤∝ positive

for 3π/2≥x≥2π, x≤∝0≤tanx≤∝ negative

 

As given cos x =1/4 is positive therefore either 0≤x≤π/2 or 3π/2≥x≥2π ,i.e., x lies either in first quadrant or in fourth quadrant. 

 

Hence the solution, too is located either in first quadrant or in fourth quadrant. 

Answer 2

Cosine is positive in the first and fourth quadrants.  Tangent is positive in the first and third quadrants.

 

Cosine and tangent are both positive only in the first quadrant.

 

Arccos(.25) = 75.5 degrees