SOLUTION: {{{tan(A)=2/3}}} A ∈ QIII, {{{sec(B)=3}}} B ∈ QI find {{{cos(A+B)}}}

Algebra.Com
Question 985175: A ∈ QIII, B ∈ QI find
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
A ∈ QIII, B ∈ QI find

.

First we draw the two angles, A, B, in their respective quadrants:

 
Draw perpendiculars to the x-axis from the end of the terminal sides of
the angles, creating right triangles.

 

For angle A:
. Since the adjacent side, x, goes left
on the x-axis, and the opposite side, y, goes downward from the x-axis, we must
consider the tangent  as  and put the numerator of ,
which is -2, on the y=OPPOSITE side and the denominator of , which is
-3, on the x=ADJACENT SIDE.

For angle B:
Since  is in QI we can leave everything positive.
We put the numerator of 3/1, which is 3, on the r=HYPOTENUSE and the denominator
of 3/1, which is 1, on the x=ADJACENT SIDE. 

Then we calculate the third sides of the two right triangles by using the
Pythagorean theorem:  

for angle A:                  for angle B:
                                          
              
                      
                       
                      
                            
                            

 

Now we are able to substitute in

 and 









Rationalizing the denominator:







Edwin

RELATED QUESTIONS

List all elements of the set A ∩ B, where A = {n ∈ N | n = 2^n − 1} and (answered by richard1234)
True or False? if A⊆B and b∈B then b∈A? (answered by vleith)
cos(A) = 9/41, with A in QI and sin(B) = -4/5 in QIII Compute the following: sin (A+B) (answered by ikleyn)
List all elements of the set A ∩ B, where A = {n ∈ N | ∃k ∈ N... (answered by robertb)
for sin a= -3/5 with terminal side in QIII and tan b= -5/12 with terminal side in QIV,... (answered by Alan3354)
For sin a=-3/5 with terminal side in QIII and tan B=-5/12 with terminal side in QIV, find (answered by Edwin McCravy)
If sin A = sqrt(10)/10 with A in QI and tan B = 4/3 with B in QI, find tan(A + B) and... (answered by ikleyn,MathTherapy)
X = {x ∈ ℕ: 2x + 8 = 0} and Y = {x ∈ ℕ : 3x – 6 = 0) Find (a) X... (answered by Fombitz)
Which of the following sets are equal? A={ 0 ,1 ,2 ,3 ,4 ,5} B={x (answered by phoihe001)