Given the right traingle with side lengths:
d, e, and f
Let's find cosx, sinx, and tanx.
From the given figure, we have:
Opposite side which is the side opposite the given angle(x) = d
Adjacent side which is the side adjacent the given angle (x) = e
Hypotenuse which is the longest side of the triangle = f
θ which is the given angle = x
To solve this, we are to apply trigonometric ratio formula for each of the following.
Thus, we have:
• a) cos x:
Apply the trigonometric ratio formula for cosine:
[tex]\cos \theta=\frac{adjacent}{\text{hypotenuse}}[/tex]
Substitute the values into the equation:
[tex]\cos x=\frac{e}{f}[/tex]
• b) sinx:
Apply the tigonometric ratio formula for sine:
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Substitute the variables into the equation:
[tex]\sin x=\frac{d}{f}[/tex]
• c) tanx:
Apply the trigonometric ratio formula for tan:
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute the variables into the equation:
[tex]\tan x=\frac{d}{e}[/tex]
ANSWER:
[tex]\begin{gathered} \cos x=\frac{e}{f} \\ \\ \\ \sin x=\frac{d}{f} \\ \\ \\ \tan x=\frac{d}{e} \end{gathered}[/tex]
