Section 5.4 I need help with 91 and 93. [ATTACH=full]1458[/ATTACH]
write the trigonometric expressions in the following forms: a) sqrt(a^2+b^2)*sin(B*theta +C) b) sqrt(a^2+b^2)*cos(B*theta-C) a* sin θ + b* cos θ ≡ R sin (θ + α) where R=sqrt(a^2+b^2) 91. given: sin(θ )+cos(θ ) a) sin(θ )+cos(θ ) =>a=1 and b=1, C=arctan (a/b)=arctan (1/1)=π/4 then r=sqrt(a^2+b^2)=sqrt(1^2+1^2)=sqrt(2) sin(theta)+cos(theta) =sqrt(2) sin(θ + π/4) b) sin(θ )+cos(θ ) =sqrt(2)*cos(theta-π/4) 93. you can do it same way
You said: sin(θ )+cos(θ ) =>a=1 and b=1, C=arctan (a/b)=arctan (1/1)=π/4 Where did C come from? Check out the link below. Verify an Identity
Moving forward, I will post questions for which Ron Larson and David Cohen (two different precalculus books) provide sample problems for. This makes a lot more sense than randomly selecting a bunch of problems for which there is nothing for me to use as a guide to answer similar problems. I am also wasting lots of time answering questions that are beyond my level of mathematics. So, skipping 93 here makes sense.