Question

If x is a positive acute angle and cos x = 3/5, find the value of sinx.

Answer 1

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 = $\dfrac{\text{adjacent}}{\text{hypotenuse}}$
sin x = $\dfrac{\text{opposite}}{\text{hypotenuse}}$

From the formula of cosine
cos x = $\dfrac{3}{5}$
$\dfrac{\text{adjacent}}{\text{hypotenuse}}= \dfrac{3}{5}$
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 = $\dfrac{\text{opposite}}{\text{hypotenuse}}$
sin x = $\dfrac{4}{5}$