Mathematics, 29.01.2020 06:43 shawnacusteroyspr8
Ihave to use trigonometric identities to solve. but i’m having trouble finding the values of cos a and sin b. can anyone me plz?
Answers: 3
![\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}](/tpl/images/0480/7600/99004.png)
![\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}](/tpl/images/0480/7600/e5910.png)
![\bf \pm\sqrt{5^2-3^2}=b\implies \pm\sqrt{16}=b\implies \pm 4=b\implies \stackrel{\textit{I~Quadrant}}{\boxed{+4=b}} \\\\[-0.35em] ~\dotfill](/tpl/images/0480/7600/b31fb.png)
![\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill](/tpl/images/0480/7600/b3927.png)
Another question on Mathematics
Mathematics, 21.06.2019 22:00
Find the maximum value of p= 4x + 5y subject to the following constraints :
Answers: 3
Mathematics, 21.06.2019 22:30
My hour hand points between the 8 and the 9 in 35 minutes it will be the next hour. what time is it ?
Answers: 2
Mathematics, 22.06.2019 01:00
Mr. t has been dating his girlfriend for one year nine months and six days how many hours has mr. t been in a relationship
Answers: 1
Mathematics, 22.06.2019 01:20
If x varies directly as y, and x = 7.5 when y = 10, find x when y = 4
Answers: 1
You know the right answer?
Ihave to use trigonometric identities to solve. but i’m having trouble finding the values of cos a a...
Questions
History, 11.02.2020 07:18
Mathematics, 11.02.2020 07:18
Mathematics, 11.02.2020 07:18
Mathematics, 11.02.2020 07:19
History, 11.02.2020 07:19
Mathematics, 11.02.2020 07:19
Mathematics, 11.02.2020 07:19
Law, 11.02.2020 07:19
