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KiRa [710]
3 years ago
5

Which expression best represents all solutions of x for the equation cot x = –1.25, where k is any integer?

Mathematics
1 answer:
Alika [10]3 years ago
5 0

Answer:

The answer is "-0.675+ k \ \pi"

Step-by-step explanation:

Given:

\to \cot \ x = - 1.25\\\\\to \cot \ x =  \cot (-0.675)\\\\\to x=  k \pi + (-0.675)\\\\\boxed{\boxed{\boxed{x=  -0.675 + k \pi}}}

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Answer: Choice C

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Explanation:

All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.

Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).

So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w

x/w is one of the answers

-----------

Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z

Therefore,

sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)

z/(y+v) is the other answer

Side note: triangle ACD is not used at all.

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