x is a positive acute angle. That means x is located in the first quadrant and has positive value in sin, cos, tan.
The formula of trigonometry ratio
cos x = [tex]\dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
sin x = [tex]\dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]
From the formula of cosine
cos x = [tex] \dfrac{3}{5}[/tex]
[tex]\dfrac{\text{adjacent}}{\text{hypotenuse}}= \dfrac{3}{5}[/tex]
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units
Draw a right triangle to illustrate the location of the sides. See image attached.
To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units
Find sin x
sin x = [tex]\dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]
sin x = [tex] \dfrac{4}{5} [/tex]
