Answer: - radical 7 / 4
Step-by-step explanation:
draw a triangle in quadrant III
plug in correct terms
use Pythagorean theorem
to simplify down to find the opposite angle
b= rad 7
The sum of the squared lengths of the other two sides of a right triangle equals the square of the hypotenuse's length, which can be defined as follows:
[tex]\to \cos \theta =-\frac{3}{4}[/tex]
[tex]\to \sin \theta =?[/tex]
[tex]\sin \theta = \frac{opposite}{hypotenuse}\\\\\cos \theta =\frac{hypotenuse}{adjacent}\\\\[/tex]
therefore
hypotenuse= -3
adjacent= 4
Using the Pythagorean theorem to find the opposite:
Hypotenuse²= Adjacent²+ Opposite²
[tex]-3^2= 4^2+x^2\\\\9=16+x^2\\\\x^2= -16+9\\\\x^2=-7\\\\x= -\sqrt{7}\\\\[/tex]
Therefore the value of sin θ [tex]= \frac{\sqrt{7}}{-3}= \frac{\sqrt{7}}{3}[/tex]
Find out more about the Pythagorean theorem here:
brainly.com/question/21332040
