cos x = 1/4 = adjacent / hypotenuse
Use pythagorean theorem to find "opposite"
(opp)^2 + (adj)^2 = (hyp)^2
(opp)^2 + (1)^2 = (4)^2
(opp)^2 + 1 = 16
(opp)^2 = 15
opp = +- sqrt 15
Since x (or theta) is in the fourth quadrant, that makes sin negative, so
opp = - sqrt 15
and
sin x = opp / hyp = (-sqrt 15) / 4
tan (pi/2 - x)
= cot x
= cos x / sin x
= (1/4) / (-sqrt 15 / 4)
= (1/4) * (4 / -sqrt 15)
= -1 / sqrt 15
= -(sqrt 15) / 15
First identify what thetta is equal to:
arccos(1/4) = 75.52 degrees.
So thetta is 75.52.
Now since pi/2 is 90 degrees, the substract 75.52 degrees from it.
And get the exact value.
tan(90-75.52) = 0.2582
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Verified answer
cos x = 1/4 = adjacent / hypotenuse
Use pythagorean theorem to find "opposite"
(opp)^2 + (adj)^2 = (hyp)^2
(opp)^2 + (1)^2 = (4)^2
(opp)^2 + 1 = 16
(opp)^2 = 15
opp = +- sqrt 15
Since x (or theta) is in the fourth quadrant, that makes sin negative, so
opp = - sqrt 15
and
sin x = opp / hyp = (-sqrt 15) / 4
tan (pi/2 - x)
= cot x
= cos x / sin x
= (1/4) / (-sqrt 15 / 4)
= (1/4) * (4 / -sqrt 15)
= -1 / sqrt 15
= -(sqrt 15) / 15
First identify what thetta is equal to:
arccos(1/4) = 75.52 degrees.
So thetta is 75.52.
Now since pi/2 is 90 degrees, the substract 75.52 degrees from it.
And get the exact value.
tan(90-75.52) = 0.2582