If (tan theta = frac{3}{4}), find the value of (sin theta + cos theta).
-
A.
(1frac{1}{3}) -
B.
(1frac{2}{3}) -
C.
(1frac{3}{5}) -
D.
(1frac{2}{5})
Correct Answer: Option D
Explanation
(tan theta = frac{opp}{adj} = frac{3}{4})
(hyp^{2} = opp^{2} + adj^{2})
(hyp = sqrt{3^{2} + 4^{2}})
= 5
(sin theta = frac{3}{5}; cos theta = frac{4}{5})
(sin theta + cos theta = frac{3}{5} + frac{4}{5})
= (frac{7}{5} = 1frac{2}{5})
There is an explanation video available below.