SOLUTION: Which of the following values of x is a solution to the equation sinx + cos x = 1? Think about the graphs of sine and cosine separately. x=45° x=90° x=135° x=180°

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Question 1182143: Which of the following values of x is a solution to the equation sinx + cos x = 1? Think about the graphs of sine and cosine separately.
x=45°
x=90°
x=135°
x=180°
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The answer will be when one of the expressions:

sin(x) or cos(x)

if ONE and the other is ZERO.

So go through those choices and find the one(s) that have (has) 1 for one of them and 0 for the other.

Edwin

Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
.
Which of the following values of x is a solution to the equation sinx + cos x = 1?
Think about the graphs of sine and cosine separately.
x=45°
x=90°
x=135°
x=180°
~~~~~~~~~~~~~~
.

Starting from

    sin(x) + cos(x) = 1,      (1)


square both sides

    sin%5E2%28x%29+%2B+2sin%28x%29%2Acos%28x%29+%2B+cos%5E2%28x%29 = 1.      (2)



Take into account that  sin%5E2%28x%29 + cos%5E2%28x%29 == 1.


You will get then from  (2)


    2*sin(x)*cos(x) = 0,

or

      sin(x(*cos(x) = 0.


So, equation (1) implies

    sin(x) = 0  or  cos(x) = 0.


It gives  x = k%2Api  or  x = pi%2F2+%2B+k%2Api,   where k is any integer number.


Checking these potential solutions,  we get the final answers  x = 2pi%2An,  or  x = pi%2F2+%2B+2pi%2An,  where n is any integer number.


Of the given four optional choices,  only  x= 90°  is the solutions to the given equation.

Solved.