Question

Find cos(A+C) given that cos A = 1/3 with A in quadrant I, and sin C = 1/4, with C in quadrant II.

Answer 1

Find $\cos(A+C)$ given that $\cos A = 1/3$ with A in quadrant I, and $\sin C = 1/4$, with C in quadrant II.

**Solution:**

$$\begin{array}{l} \cos(a + c) = \cos a \cos c - \sin a \sin c = \left(\frac{1}{3}\right) \left(-\frac{\sqrt{(15)}}{4}\right) - \left(\frac{1}{4}\right) \left(\frac{\sqrt{(8)}}{3}\right) = \left(\frac{1}{12}\right) \left(-\sqrt{(15)} - 2\sqrt{2}\right) = -0.56. \end{array}$$

Answer: $\cos(a + c) = -0.56$.