Question

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

Approach

Given $tan θ = \frac{24}{7}$ , construct a right triangle with opposite = 24 and adjacent = 7. By Pythagorean theorem, hypotenuse = 25. Then $sin θ = \frac{24}{25}$ and $cos θ = \frac{7}{25}$ , so $sin θ + cos θ = \frac{31}{25}$ .

Step-by-step working

1
$tan θ = \frac{24}{7}$ , so in a right triangle, opposite = 24, adjacent = 7, hypotenuse = $2 4^{2} + 7^{2} = 25$
1.5 marks
2
$sin θ + cos θ = \frac{24}{25} + \frac{7}{25} = \frac{31}{25}$
0.5 marks

Concepts used

trigonometric ratiostan thetacot thetafind valuetrigonometric identity

Approach

Step-by-step working

Concepts used

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