mramosoy1byo
contestada

Solve the following equation in the interval [0, 2 π]. Note: Give the answer as a multiple of π. Do not use decimal numbers. The answer should be a fraction or an integer. Note that π is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is π/2 you should enter 1/2. If there is more than one answer enter them separated by commas. (sin(t))^2=3/4

Respuesta :

[tex]\bf [sin(t)]^2=\cfrac{3}{4}\implies sin^2(t)=\cfrac{3}{4}\implies sin(t)=\pm\sqrt{\cfrac{3}{4}} \\\\\\ sin(t)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(t)=\pm\cfrac{\sqrt{3}}{2}\implies \measuredangle t= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]
yoodyannapolis

The solution to the equation [tex]\sin(t))^2=\frac{3}{4}[/tex] is[tex]t=\frac{\pi}{3} ,\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}[/tex].

We have  equation [tex]\sin(t))^2=\frac{3}{4}[/tex]

The sine function is positive in the first and the second quadrant.

Solving this equation

[tex](\sin(t))^2=\frac{3}{4}\\\sin(t)=\pm\frac{\sqrt{3} }{\sqrt{4} }\\\sin(t)=\pm\frac{\sqrt{3} }{2}\\t=\frac{\pi}{3} ,\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}[/tex]

Th values of t in [0, 2π] is[tex]t=\frac{\pi}{3} ,\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}[/tex]

Learn more:https://brainly.com/question/8120556

Otras preguntas