Question

Use the given information to find (a) sin (s +t), (b) tan (s + t), and (c) the quadrant of s+t. 12 13 and sint = 5 s and t in quadrant III 4 COS S =- (a) sin (s+t)=0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (b) tan (s+t) = 0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (c) What is the quadrant of s +t? O Quadrant Quadrant II O Quadrant III Quadrant IV

Answer 1

and sint= - COSS S-12 Given - 1 2 3 WC know that cos's + sin's & sins = 1 VI-coss sins - Via 1-(-1315 sins - + V1-144 165-145 169 Ic5 25 163 Since s is in quadrant 111. So in quadrant 111 sins with be negative Hence sins Again sost+ sintai I Vi-sint 3 I VI-645) Costa i-== V Is LS-14 - vis costa + 3/5 since t is in quadrant n. so cost in quadrant 1. .. cost = -3/5 will be negatik

since Cossa - Sins i sinta -45, cost = -3/5 and tans sins coss = 11/13 = 23 x 1 12 + 13 음 45** = 443 tant sint cost = +415 = +3/5 (a) We know that NOW sin(Stt) = (sin s) Cost) + (OSS) (sint) = (3)=6**) + (-43)* (**) + 15 .65 + 48 65 (15+48 65 63 65 Sincs+t) Theory 63 65

(62 tan (5++) 3 fan(s) + fanct); 1-ans.fant is + 5+16 12 34 T (3 16 T유상 34 -20 36 tan (5+ t) 63 16 (c) since sin (S++) is and tan (set) is positive positive [: All trig function is positive in test quadranti I] So (Ste) in quadrant I Ans Quadrant I