Answer:
x= 150º
Step-by-step explanation:
1. (90-x)º = -60º
2. -x = -150º
3. x= 150º
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of x for whicht the given equation cot(90°−x)= –3/√3 will be satisfied is -60°.
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The value of x that satisfies cot(90°−x)= –3/√3 can be solved as,
cot(90°−x) = (-3/√3)
tan(x) = (-3/√3)
x = tan⁻¹ (-3/√3)
x = tan⁻¹ (-√3)
x = -60° +180n
x = -60°
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
#SPJ2
