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Hello, find the exact value of each of the following under the given conditions. sin alpha=3/5, 0<alpha<pi/2  ;   cos beta= (8sqrt113)/113, -pi/2<beta<0 (a) sin (alpha+beta)= -(4sqrt113)/565(b) cos (alpha+beta)= (53sqrt113)/565(c) sin (alpha-beta)= (52sqrt113)/565(d) tan (alpha-beta)= ? I got the answers for (a to c), the correct answers, but I couldn't get (d) correct. I got the answer 53/4 instead of 52/11, which is the correct answer for (d). I used the sum and difference formulas for each of them, yet I don't understand how 52/11 is the correct answer. Can you explain how it is 52/11?

Question

Hello, 

find the exact value of each of the following under the given conditions. 

sin alpha=3/5, 0<alpha<pi/2  ;   cos beta= (8sqrt113)/113, -pi/2<beta<0

 

(a) sin (alpha+beta)= -(4sqrt113)/565

(b) cos (alpha+beta)= (53sqrt113)/565

(c) sin (alpha-beta)= (52sqrt113)/565

(d) tan (alpha-beta)= ? 

I got the answers for (a to c), the correct answers, but I couldn't get (d) correct. I got the answer 53/4 instead of 52/11, which is the correct answer for (d). I used the sum and difference formulas for each of them, yet I don't understand how 52/11 is the correct answer. Can you explain how it is 52/11?

check_circleAnswer
Step 1

We have to find value of tan(alpha-beta).

Information is given below:

3
sin(a) 0a<
8VI13
2
cos(B)
113
2
tan(a )?
help_outline

Image Transcriptionclose

3 sin(a) 0a< 8VI13 2 cos(B) 113 2 tan(a )?

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Step 2

We will use following formula.

Formula is given below:

tan(a)tanp)
tan(a )1+ tan(@) tan(B)
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Image Transcriptionclose

tan(a)tanp) tan(a )1+ tan(@) tan(B)

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Step 3

Now use pythagorean theorem to find remaining sides of right angle triangles with angle alpha and beta.

alpha in ...

113
5
3
8(113)^.5
4
7(113)^.5
3
where 0 < a<
tan (a)
4
7
(Bin quadrant 4) where ß in
2
tan()
8
11
help_outline

Image Transcriptionclose

113 5 3 8(113)^.5 4 7(113)^.5 3 where 0 < a< tan (a) 4 7 (Bin quadrant 4) where ß in 2 tan() 8 11

fullscreen

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Math

Calculus

Functions

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