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

• Random-Hero-
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.
Random-Hero-

## 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!

Let's start with part a). Have you thought about $$sin^2(x) + cos^2(x) = 1$$?

Holy smoke I can't believe I missed that! thanks hitman! I owe you one!

Now for the last 2 lil buggers!

well I got a and b, now how would I do c? :|

Nevermind, I got it, thanks for your help hitman! I don't know how on Earth i missed that!

sin(x+y) = sinx*cosy+siny*cosx

## 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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