Mathematics

Problem

For two angles

\alpha

and

\beta

the following information is given:

\sin \alpha=\dfrac45

with

90^\circ<\alpha<180^\circ

, and

\cos \beta=\dfrac{5}{13}

with

270^\circ<\beta<360^\circ

. Using these data, find the exact values of: a. (i)

\cos \alpha

and

\sin \beta

b. (ii)

\sin(\alpha+\beta)

c. (iii)

\cos(\alpha-\beta)

d. (iv)

\tan(\alpha+\beta)