Given:
[tex]cos\theta=\frac{3}{5}[/tex]
Let's solve for tan(θ).
Apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{\text{ adjacent}}{hypotenuse}=\frac{3}{5}[/tex]
Hence, we have:
Adjacent = 3
Hypotenuse = 5
Now, let's find the opposite side using Pythagorean Theorem:
[tex]\text{ opposite = }\sqrt{(hypotenuse)^2-(adjacent)^2}[/tex]
Thus, we have:
[tex]\begin{gathered} \text{ opposite = }\sqrt{5^2-3^2} \\ \\ \text{ opposite = }\sqrt{25-9} \\ \\ \text{ opposite = }\sqrt{16}=4 \end{gathered}[/tex]
Therefore, the opposite side is 4 units.
Apply the trigonometric ratio formula for tangent:
[tex]tan\theta=\frac{\text{ opposite }}{adjacent}[/tex]
Where:
Opposite = 4
Adjacent = 3
Hence, we have:
[tex]tan\theta=\frac{4}{3}[/tex]
Therefore, the answer is:
tanθ = 4/3
ANSWER:
4/3
