Question

Fill in the blank. If necessary, use the slash mark ( 7 ) for a fraction bar. if cose = , then tang =

Answer 1

Given:

`cos\theta=(3)/(5)`

Let's solve for tan(θ).

Apply the trigonometric ratio formula for cosine:

`cos\theta=\frac{\text{ adjacent}}{hypotenuse}=(3)/(5)`

Hence, we have:

Adjacent = 3

Hypotenuse = 5

Now, let's find the opposite side using Pythagorean Theorem:

`\text{ opposite = }√((hypotenuse)^2-(adjacent)^2)`

Thus, we have:

`\begin{gathered} \text{ opposite = }√(5^2-3^2) \\ \\ \text{ opposite = }√(25-9) \\ \\ \text{ opposite = }√(16)=4 \end{gathered}`

Therefore, the opposite side is 4 units.

Apply the trigonometric ratio formula for tangent:

`tan\theta=\frac{\text{ opposite }}{adjacent}`

Where:

Opposite = 4

Adjacent = 3

Hence, we have:

`tan\theta=(4)/(3)`

Therefore, the answer is:

tanθ = 4/3

ANSWER:

4/3