Ngles α and β are angles in standard position such that: α terminates in quadrant iii and sinα = -5/13 β terminates in quadrant ii and tanβ = -8/13 find cos(α - β).

0.5848

Step-by-step explanation:

Sin α=-5/13--> arcsin(-5/13)=α and we know that α is in quadrant III  and because of trigonometry properties we know that sinα can be negative just in quadrant III and IV. There are two options so we choose the option of quadrant III.  α≅202,6°

Tanβ=-8/13---> arctang(-8/13)=β and we know that β is in quadrant II  and because of trigonometry properties we know that tanβ can be negative just in quadrant II and IV. There are two options so we choose the option of quadrant II. β≅148,39°

cos(α-β)=cos(202,6°-148,39)≅0.5848

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

answer is : muchas/tipicas

have a nice day!

~recklesschicken