Given sinx=4/5, cosy = 7/25. Find the following

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In summary, The values of angles x and y are given, and the goal is to find the exact values of cosine of x, sine of y, and sine of the sum of x and y. Using the formula sin^2(x) + cos^2(x) = 1, the exact values for cosine of x and sine of y can be determined. For the final part, the formula sin(x+y) = sinx*cosy+siny*cosx can be used to find the exact value of sine of the sum of x and y.
  • #1
Random-Hero-
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Homework Statement



Angles x and y are located in the first quadrant such that sinx=4/5, and cosy = 7/25.

a) Determine an exact value of cosx.

b) Determine an exact value of siny.

c) Determine an exact value for sin(x+y)


Homework Equations



Compound angle formulas perhaps? I don't really know, that's the problem!

The Attempt at a Solution



I'm really at a loss here, do I just sub those into some formula or something? Can anyone help me out? Or get me pointed in the right direction? thanks in advance!
 
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  • #2
Let's start with part a). Have you thought about [tex] sin^2(x) + cos^2(x) = 1 [/tex]?
 
  • #3
Holy smoke I can't believe I missed that! thanks hitman! I owe you one!

Now for the last 2 lil buggers!
 
  • #4
well I got a and b, now how would I do c? :|
 
  • #5
Nevermind, I got it, thanks for your help hitman! I don't know how on Earth i missed that!
 
  • #6
sin(x+y) = sinx*cosy+siny*cosx
 

Related to Given sinx=4/5, cosy = 7/25. Find the following

1. What is the value of tanx?

The value of tanx can be found by dividing sinx by cosy, which gives us tanx = (4/5)/(7/25) = 4/7.

2. What is the value of secx?

The value of secx can be found by taking the reciprocal of cosx, which gives us secx = 1/cosx = 1/(7/25) = 25/7.

3. What is the value of cscx?

The value of cscx can be found by taking the reciprocal of sinx, which gives us cscx = 1/sinx = 1/(4/5) = 5/4.

4. What is the value of cotx?

The value of cotx can be found by dividing cosy by sinx, which gives us cotx = (7/25)/(4/5) = 7/20.

5. What is the value of secx + cscx?

The value of secx + cscx can be found by substituting the previously calculated values, which gives us secx + cscx = 25/7 + 5/4 = (100+35)/28 = 135/28.

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