Anjela R.

asked • 02/12/22

If sin(𝜃)<0, find the value of cos(𝜃) when cot(𝜃)=3/7. (Give an exact answer. Use symbolic notation and fractions where needed.) cos(𝜃) =

Brenda D.

tutor
Are you referring to a Right Triangle? If so, the cot = cos/sin = adj/opp, and if the sin is negative, in order for the cot to be positive one would need have the situation where a (negative)/(negative) = positive. Also cot=1/tan. For a Right Triangle, the ratio above gives the sides of the two shorter legs; you need to calculate the hypotenuse to obtain the cosine. You can also find the value of the angle whose cot is 3/7, then look up the cosine. Hope this helps.
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02/12/22

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Beth B. answered • 02/12/22

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The cotangent of angle Θ = 3/7

cot(Θ) = 3/7


Cotangent = adjacent side/opposite side = 3/7

∴ tangent of Θ = 7/3


Length of hypotenuse = √(32 + 72) = √58


From the given info we know that the adjacent side length is 3.


Cos Θ = adjacent/Hypotenuse = 3/(√58)


Now, we know that the Sine of Θ is less than 0 or NEGATIVE, so the Cosine is also less than 0 or NEGATIVE.


∴ cos Θ = -3/√58




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