Question 1122860
The graph of y=cos (θ + pi/2) is a reflection of the graph of y= -sin θ in the x-axis. 


i would say false.


these equations are identical.


if theta = pi/4 (45 degrees), then:


cos(pi/4 + pi/2) = -.7071067812


= sin(pi/4) = -.7071067812


this occurs at all values of theta.


the equations of y = cos(theta + pi/2) and y = sin(theta) would be reflections about the line = x.


the following graphs show the relationships.


in both graphs, i used x instead of theta, since x can be graphed easier than theta.


theta and x mean the same thing.
they are the angle being measured.


first graph is y = cos(x + pi/2) and y = -sin(x)


both equations give you the same graph which means the equations are equivalent.


<img src = "http://theo.x10hosting.com/2018/091201.jpg" alt="$$$" >


second graph is y = cos(x + pi/2) and y = sin(x).


in this graph it is clear to see that the graph of y = sin(x) is a reflection of the graph y = cos(theta + pi/2) about the x-axis.


<img src = "http://theo.x10hosting.com/2018/091202.jpg" alt="$$$" >



On the interval -pi < &#952; < pi, the only intersection point of the graphs of y= &#952; amd y= sin &#952; is at 0=0.


this statement is true as can be seen in the following graph.


in the graph, x represents theta.
they mean the same thing.


you can see that when x is 0, y = sin(x) is equal to 0 and y = x is also equal to 0.


at any other point on the graph, y = x is not equal to y = sin(x).


the graph would ahow all the intersection points between the two equations and only one is shown at x = 0.


<img src = "http://theo.x10hosting.com/2018/091203.jpg" alt="$$$" >L


Given the right triangle ABC, fill the values of sin &#952; and cos &#952;, and prove that sin^2 &#952; + cos^2 &#952;= 1


in triangle ABC, side a is opposite angle A, side b is opposite angle B and side c is opposite angle C.


the hypotenuse of the triangle is the side opposite angle C which is the right angle in the triangle.


by pythagorus, c^2 = a^2 + b^2


that's a given.


you also know that sin(A) = opposite / hypotenuse = a/c and cos(A) = adjacent / hypotenuse = b/c


in sin(A) = a/c, you can solve for a to get a = c * sin(A).


in cos(A) = b/c, you can solve for b to get b = c * cos(A).


in the formula c^2 = a^2 + b^2, you can replace a with c * sin(A) and you can replace b with c * cos(A) to get:


c^2 = (c*sin(A))^2 + (c*cos(A))^2


this becomes:


c^2 = c^2 * sin^2(A) + c^2 * cos^2(A)


divide both sides of this equation by c^2 and you get:


1 = sin^2(A) + cos^2(A)


QED


the definition of QED is:


QED is an abbreviation of the Latin words "Quod Erat Demonstrandum" which loosely translated means "that which was to be demonstrated". It is usually placed at the end of a mathematical proof to indicate that the proof is complete.