In quadrant 4, we need to graph a reference right triangle:
Where cosθ= adjacent side/ hypotenuse . Therefore, 2 is the value for the adjacent side and the hypotenuse is equal to 7.
Now, to find the opposite side, we need to use the Pythagorean theorem:
[tex]c^2=a^2+b^2[/tex]Where c represents the hypotheses,
a represents the adjacent side and b represents the opposite side.
Solve the equation for b, then:
[tex]b=\sqrt[]{c^2-a^2}[/tex]Replacing the values:
[tex]b=\sqrt[]{(7)^2-(2)^2}[/tex]Hence:
[tex]b=3\sqrt[]{5}[/tex]Finally, we have that sin(theta)= opposite side / hypotenuse.
Replacing with the values, therefore:
[tex]\sin \theta=\frac{3\sqrt[]{5}}{7}[/tex]
