find tan(-x) if cot (pi/2 -x)=-1.84
To find tan(-x), we can use the fact that tan(-x) = -tan(x).
Given that cot(pi/2 - x) = -1.84, we know that tan(pi/2 - x) = 1/cot(pi/2 - x) = -1/(-1.84) = 0.5435.
Since tan(pi/2 - x) = cot(x), we have tan(x) = 0.5435. Therefore, tan(-x) = -tan(x) = -0.5435.
To find tan(-x) when cot(pi/2 - x) = -1.84, we can use the relationship between cotangent and tangent:
cot(pi/2 - x) = -1.84
Since cot(pi/2 - x) is the reciprocal of tan, we can rewrite the equation as:
1/tan(pi/2 - x) = -1.84
Now, we can take the reciprocal of both sides of the equation:
tan(pi/2 - x) = -1/1.84
Simplifying further:
tan(pi/2 - x) = -25/46
Since tan(pi/2 - x) represents the tangent of an angle, we can find its reference angle by finding the complementary angle, which is (pi/2 - x).
The reference angle, let's call it y, is given by:
y = pi/2 - x
So, we can write:
tan(y) = -25/46
Now, we can take the inverse tangent (arctan) of both sides of the equation:
y = arctan(-25/46)
Finally, we can find -x by subtracting y from pi/2:
-x = pi/2 - y
Therefore, tan(-x) is tan(pi/2 - y), which simplifies to tan(pi/2 - arctan(-25/46)).
To find the value of tan(-x) given that cot(pi/2 - x) = -1.84, we can use the trigonometric identities relating cotangent and tangent.
Cotangent and tangent are reciprocal functions, meaning that cot(x) = 1/tan(x) and tan(x) = 1/cot(x).
We are given that cot(pi/2 - x) = -1.84. This implies that cot(pi/2 - x) = 1/tan(pi/2 - x).
To find tan(pi/2 - x), we can take the reciprocal of -1.84:
1/tan(pi/2 - x) = -1.84
Now, we can solve for tan(pi/2 - x):
tan(pi/2 - x) = 1/(-1.84)
tan(pi/2 - x) = -0.543478
Therefore, tan(-x) = tan(-1 * x) = -tan(x) = -(-0.543478) = 0.543478.
So, tan(-x) is approximately equal to 0.543478.