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If tan(pi/2 - x) = -0.34, find cot x?

Author :

Submitted : 2018-06-14 06:02:38    Popularity:     

Tags: pi  tan  0.34  cot  find  

Please explain :)

Answers:

Tan (pi/2 - x) =>
Hence
Cot ( pi/2 - x( = - 1/0.34 = -100/34 = -50/17
Cos (pi/2 - x) / Sin(pi/2 - x) = -50/17

Cs(pi/2)CosX + Sin(pi/2)SinX ) / (in(pi/2)CosX - Cos(pi/2)SinX ) = -50/17
(0)CosX + (1)SinX) / (1)CosX - (0)SinX) = -50/17
SinX / Cos X = -50/17
TanX = -50 / 17
Cot(X) = -17/50 = -0.34

tan(pi/2-x) = -0.34
pi/2-x = tan^-1(-0.34)
pi/2-x = -0.32774
x = pi/2 + 0.32774
x= 1.8985
cot(x) = cot(1.8985) = -0.34

If tan(pi/2 - x) = -0.34
We know that If tan(pi/2 - x) =cot x
Hence tan(pi/2 - x) = -0.34 then cotx= -0.34

.
If the question is to understand why tan(½π - x) = cot(x), then we will go through this step by step:
We know that;
sin(A - B) = sinAcosB - cosAsinB
and
cos(A - B) = cosAcosB + sinAsinB

sin(½π - x)
= sin(½π)cos(x) - cos(½π)sin(x)
= cos(x) - 0
= cos(x)

cos(½π - x)
= cos(½π)cos(x) + sin(½π)sin(x)
= 0 + sin(x)
= sin(x)

Then
tan(½π - x) = -0.34
sin(½π - x) / cos(½π - x) = -0.34
cos(x) / sin(x) = -0.34
cot(x) = -0.34
━━━━━━

cot(x) = tan(π/2 - x) = -0.34



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