Find the exact value of tan(x-y) if sinx=8/17 and cosy=3/5

2 answers:

8 0

To solve the the question we proceed as follows:
From trigonometric laws
(cos x)^2+(sin x)^2=1
(cos y)^2+(sin y)^2=1
sin (x-y)=sin x sin y-sin y cos x
cos (x-y)=cos x cos y+ sin x sin y
si x=8/17
cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(225/289)=15/17
cos y=3/5
sin x= sqrt(1- (cos x)^2)= sqrt(1-9/25)=sqrt(16/25)=4/5
thus
tan (x-y)=[sin (x-y)]/[cos (x-y)]
=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]
plugging in the values we obtain:
[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]
simplifying
[24/85-60/85]/[45/85+32/85]
=-36/77

makkiz [27]2 years ago

6 0

Answer:

Step-by-step explanation:

You might be interested in

A linear function, f, has an x-intercept at (5,0) and a y-intercept at (0,3). Which best describes the shape of the graph of thi

deff fn [24]

From this statement, you can conclude that this is a negative linear function because the x-intercept is to the right of the y-intercept.

Hope this helps!

8 0

3 years ago

Read 2 more answers

What is the solution of the proportion? 14/12 = D/48 a. 56 b. 672 c. 168 d. 576

Verdich [7]

So basically we can simplify the fraction by finding the gcf which is the greatest common factor so 14/12 both have 2 in common we simplify that by dividing by 2 so 14÷2 is 7/6 is the fraction on the left hand side and d/48 is the fraction on the right hand side so to solve for d we have to divide 336/6 whixh equals 56 as tour answer. Hoped this helped!!

8 0

3 years ago

Read 2 more answers

If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)

krok68 [10]

$Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$