+0  
 
0
760
2
avatar

Cos (a+b) sin a=-3/5 sin b=-5/13 a & b in Q3

Guest Jul 22, 2014

Best Answer 

 #1
avatar+93305 
+8

Sin(a) and sin(b) are both negative which means that a and b have to be in the 3rd or 4th quadrant.

 

 $$cos(a+b)\\\\
=cos(a)cos(b)-sin(a)sin(b)\\\\
=\pm\frac{4}{5}\times \pm \frac{12}{13}- \;\;\frac{-3}{5}\times \frac{-5}{13}\\\\
=\pm\frac{48}{65}- \;\;\frac{15}{65}\\\\
=\frac{-15-48}{65}\;\;or\;\;\frac{-15+48}{65}\\\\
=\frac{-63}{65}\;\;or\;\;\frac{33}{65}\\\\$$

Melody  Jul 23, 2014
 #1
avatar+93305 
+8
Best Answer

Sin(a) and sin(b) are both negative which means that a and b have to be in the 3rd or 4th quadrant.

 

 $$cos(a+b)\\\\
=cos(a)cos(b)-sin(a)sin(b)\\\\
=\pm\frac{4}{5}\times \pm \frac{12}{13}- \;\;\frac{-3}{5}\times \frac{-5}{13}\\\\
=\pm\frac{48}{65}- \;\;\frac{15}{65}\\\\
=\frac{-15-48}{65}\;\;or\;\;\frac{-15+48}{65}\\\\
=\frac{-63}{65}\;\;or\;\;\frac{33}{65}\\\\$$

Melody  Jul 23, 2014
 #2
avatar+20008 
+5

Cos (a+b) sin a=-3/5 sin b=-5/13 a & b in Q3  ?

$$\boxed{\cos(a+b)=\;?} \quad \sin{(a)} =-{3\over5} \qquad \sin {(b)}=-{5\over13}$$

$$\cos{(a+b)}=\cos{(a)}*\cos(b)-sin{(a)}*\sin{(b)}$$

cos(a)=?   and   cos(b)=?

$$\textstyle{
\cos{(a)}=\sqrt{1-\sin^2{(a)}}=
\sqrt{1-({3\over5})^2}= {\sqrt{5^2-3^2}\over5}={\sqrt{16}\over5}={\pm4\over5}=\pm{4\over5}
}$$

$$\textstyle{
\cos{(b)}=\sqrt{1-\sin^2{(b)}}=
\sqrt{1-({5\over13})^2}= {\sqrt{13^2-5^2}\over13}={\sqrt{144}\over13}={\pm12\over13}=\pm{12\over13}
}$$

$$\cos{(a+b)}=\pm
({4\over5})
\times
({12\over13})
-
(-{3\over5})
\times
(-{5\over13})$$

$$\cos{(a+b)}=\pm
({4\over5})
\times
({12\over13})
-
({3\over5})
\times
({5\over13})$$

$$\cos{(a+b)}=({\pm(4*12)\over5*13})
-
({3*5\over5*13})$$

$$\cos{(a+b)}={\pm(4*12)-3*5\over5*13}$$

$$\cos{(a+b)}={\pm48-15\over65}$$

$$\text{1.) }\cos{(a+b)}={48-15\over65}={33\over65}=0.50769230769$$

$$\text{2.) }\cos{(a+b)}={-48-15\over65}=-{63\over65}=-0.96923076923$$

heureka  Jul 23, 2014

17 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.