Question #9d772

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Answer 1 · 2018-01-29T02:26:03

#cot(x)= sqrt35/35#

Given: #cos(x)= 1/6# and #sin(x) = sqrt35/6#

When given both the sine and the cosine functions, one should to verify that #cos^2(x)+sin^2(x) = 1#:

#(1/6)^2+(sqrt35/6)^2 = 1#

#1/36+35/36 = 1#

#36/36 = 1# verified.

Use the identity, #cot(x) = cos(x)/sin(x)#:

#cot(x)= (1/6)/(sqrt35/6)#

Multiply by 1 in the form of #6/6#:

#cot(x)= 1/sqrt35#

Rationalized the denominator:

#cot(x)= sqrt35/35#