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

Fill in the blank. If necessary, use the slash mark ( 7 ) for a fraction bar. if cose-example-1

1 Answer

6 votes

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

User Pgiitu
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