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).

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

we can use triangle and find cos(α)

we get

and we have

we can draw triangle

now, we can use formula

now, we can plug values

now, we can simplify it

...............Answer

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12