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aev [14]
3 years ago
15

Solve the equation for 0° ≤ x ≤ 90°. Round to the nearest degree. 8cotθ + 3 = 5

Mathematics
1 answer:
galina1969 [7]3 years ago
5 0

<u><em>Answer:</em></u>

θ = 76°

<u><em>Explanation:</em></u>

<u>The given equation is:</u>

8 cotθ + 3 = 5

8 cotθ = 5-3

8 cotθ = 2

cot θ = \frac{2}{8} = \frac{1}{4}

<u>Now, we find θ</u>

We know that the cot function is the inverse of the tan function.

The tan of an angle is positive in the first and third quadrants, therefore, the cot will be <u>positive</u> in the <u>first and third quadrants</u> as well

<u>Now, we are given the condition:</u>

0° ≤ x ≤ 90°

<u>Therefore, we know for sure that our angle is in the first quadrant</u>

θ = cot⁻¹(\frac{1}{4}) = 75.96° = 76° to the nearest degree

Hope this helps :)

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