If (sintheta = frac{3}{5}, 0° < theta < 90°), evaluate (cos(180 – theta)).
-
A.
(frac{4}{5}) -
B.
(frac{3}{5}) -
C.
(frac{-3}{5}) -
D.
(frac{-4}{5})
Correct Answer: Option D
Explanation
Given (sin theta = frac{3}{5} implies opp = 3, hyp = 5)
Using Pythagoras’ Theorem, we have ( adj = sqrt{5^{2} – 3^{2}} = sqrt{16} = 4)
(therefore cos theta = frac{4}{5}, 0° < theta < 90°)
In the quadrant where (180° – theta) lies is the 2nd quadrant and here, only (sin theta = +ve).
(therefore cos (180 – theta) = -ve = frac{-4}{5})