Find all solutions of the equation in the interval [0, 2π). cotθ+ √3= 0
1 answer:
Answer:
{5π/6, 11π/6}
Step-by-step explanation:
Since you have memorized the trig values of common angles, you know tan(π/6) = 1/√3, so cot(π/6) = √3.
The solution to this equation is ...
cot(θ) = -√3
so θ = -π/6 or, in the domain of interest, 11π/6. There is a corresponding quadrant II angle, 5π/6.
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Step-by-step explanation:
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![x+y=25 \\ y=25-x~~Other~number~in~terms~of~x \\ \\ x^2+y^2=313 \\ x^2+2xy+y^2=313+2xy \\ (x+y)^2=313+2x(25-x) \\ \frac{25^2-313}{2} =25x-x^2 \\ x^2-25x+156 \\ \\ \Delta =(-25)^2-4\times 1\times 156 \\ \Delta =625-624 \\ \sqrt{\Delta}=1 \\ \\ x= \frac{25 \pm 1}{2} \\ x= \left \{ {{x_1=13} \atop {x_2=12}} \right.](https://tex.z-dn.net/?f=x%2By%3D25%20%5C%5C%20y%3D25-x~~Other~number~in~terms~of~x%20%5C%5C%20%5C%5C%20x%5E2%2By%5E2%3D313%20%5C%5C%20x%5E2%2B2xy%2By%5E2%3D313%2B2xy%20%5C%5C%20%28x%2By%29%5E2%3D313%2B2x%2825-x%29%20%5C%5C%20%5Cfrac%7B25%5E2-313%7D%7B2%7D%20%3D25x-x%5E2%20%5C%5C%20x%5E2-25x%2B156%20%5C%5C%20%5C%5C%20%5CDelta%20%3D%28-25%29%5E2-4%5Ctimes%201%5Ctimes%20156%20%5C%5C%20%5CDelta%20%3D625-624%20%5C%5C%20%5Csqrt%7B%5CDelta%7D%3D1%20%5C%5C%20%5C%5C%20x%3D%20%5Cfrac%7B25%20%5Cpm%201%7D%7B2%7D%20%5C%5C%20x%3D%20%5Cleft%20%5C%7B%20%7B%7Bx_1%3D13%7D%20%5Catop%20%7Bx_2%3D12%7D%7D%20%5Cright.)
The number "x" is given by:
Therefore, we have: