Question

If $tan θ = \frac{24}{7}$ , then find the value of $sin θ + cos θ$ .

Approach

Given $tan θ = \frac{24}{7}$ , we use the Pythagorean identity to find $sin θ = \frac{24}{25}$ and $cos θ = \frac{7}{25}$ . Then $sin θ + cos θ = \frac{31}{25}$ .

Step-by-step working

1
From $tan θ = \frac{24}{7} = \frac{P}{B}$ , construct a right triangle with opposite = 24 and adjacent = 7.
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2
Calculate hypotenuse: $H = 2 4^{2} + 7^{2} = 576 + 49 = 25$ .
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3
Find $sin θ = \frac{24}{25}$ and $cos θ = \frac{7}{25}$ .
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4
Compute $sin θ + cos θ = \frac{24}{25} + \frac{7}{25} = \frac{31}{25}$ .
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Concepts used

trigonometric ratiostan thetacot thetasin thetacos thetaevaluate

Approach

Step-by-step working

Concepts used

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