If tanθ = \frac{4}{3} then (sin θ + cos θ) = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If $tanθ = \frac{4}{3}$ then (sin θ + cos θ) = ?

$\frac{7}{3}$

$\frac{7}{4}$

$\frac{5}{7}$

$\frac{7}{5}$

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Given tanθ = 4/3, we can construct a right triangle where the opposite side is 4 and the adjacent side is 3. The hypotenuse is then √(4²+3²) = √(16+9) = √25 = 5.

Therefore, sinθ = opposite/hypotenuse = 4/5 and cosθ = adjacent/hypotenuse = 3/5.

Now, sinθ + cosθ = 4/5 + 3/5 = $\frac{7}{5}$ .

Final Answer: $\frac{7}{5}$