Chapter1 (Q7) Use the given information to find a) Sin (s + t ) b, Tan ( s + t) and c) the quadrant of s + t .a. \(Cos s=15/17 and sint=4/5,s in quadrant 2 and t in quadrant 1. \)b. \(Sin s=2/3 and sint=-1/3,s in quadrant 2 and t in quadrant 1.\)c. \( Cos s=-1/5 and sint=3/5,s in and t in quadrant 2.\)

Solution

\( SinS=√(1-cos^2 ) s←√(1-(225/289))=8/17 .

cost=√(1-sin^2 ) t←√(1-(16/25))=-3/5

Sin (s+t)=Sinscost+Cosssint

Cos (S+t)=8/17 ×(-3/5)+(15/17)×(4/5)=-24/85-60/85 \)=

b. \(Sin s=2/3 and sint=-1/3,s in quadrant 2 and t in quadrant 1.\)

Solution

\( CosS=√(1-cos^2 ) s←√(1-(4/9))=√5/3 .

cost=√(1-sin^2 ) t←√(1-(1/9))=-√8/3.

Sin (s+t)=Sinscost-Cosssint

Sin(S+t)=2/3 ×(-√8/3)+√5/3×(-1/3 \))=

c. \( Cos s=-1/5 and sint=3/5,s in and t in quadrant 2.\)

Solution

\( SinS=√(1-cos^2 ) s←√(1-(1/25))=√24/25 .

cost=√(1-sin^2 ) t←√(1-(9/25))=-4/5

Sin (s+t)=Sinscost+Cosssint

SinS (S+t)=√24/25 ×(-4/5)+(-1/5)×(3/5)=-(4√24)/125-3/25 \)=

Solution

a. Cos (S+t)=8/17×(-3/5)+(15/17)×(4/5)=-24/85-60/85=(-24+60)/85=36/85.

b. Sin(S+t)=2/3 ×(-√8/3)+√5/3×(-1/3)=-(2√8)/9-√5/9=(-2√8-√5)/9.

c. SinS (S+t)=√24/25×(-4/5)+(-1/5)×(3/5)=-(4√24)/125-3/25=-(4√24-15)/125.