Question

Angles α and β are angles in standard position such that: α terminates in Quadrant II and sinα = 3/5, β terminates in Quadrant I and cosβ = 4/5 Find cos(α + β).

Answer 1

We are given

Angles α and β are angles in standard position

and

α terminates in Quadrant II

β terminates in Quadrant I

and we have

$sin(\alpha)=\frac{3}{5}$

we can use triangle and find cos(α)

we get

$cos(\alpha)=-\frac{4}{5}$

and we have

$cos(\beta)=\frac{4}{5}$

we can draw triangle

$sin(\beta)=\frac{3}{5}$

now, we can use formula

$cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta)$

now, we can plug values

$cos(\alpha+\beta)=-\frac{4}{5}\times \frac{4}{5}-\frac{3}{5}\times \frac{3}{5}$

now, we can simplify it

$cos(\alpha+\beta)=-\frac{16}{25}-\frac{9}{25}$

$cos(\alpha+\beta)=-\frac{(16+9)}{25}$

$cos(\alpha+\beta)=-\frac{(16+9)}{25}$

$cos(\alpha+\beta)=-\frac{25}{25}$

$cos(\alpha+\beta)=-1$...............Answer