a. Use graphs to decide if the equation is an identity.
b. If the equation is not an identity, find a value of the variable that makes the equation false.
sin(pi/2+Beta)=1+sinBeta
Without even graphing it, I can tell they are not an identity,
y = 1 + sinB would be the graph of y = sinB moved vertically by 1 unit
y = sin(B + π/2) would be the graph of y = sinB moved horizontally π/2 units to the left.
Two entirely different graphs.
test with π/2
LS = sin(π/2+π/2
= sin π = 0
RS = 1 + sin(π/2)
= 1 + 1 = 2 ≠ LS
To determine if the equation sin(pi/2+Beta) = 1 + sinBeta is an identity, we can use graphs. Here's how you can do it:
1. First, choose a range of values for the variable Beta. For example, you can choose -2π to 2π or -360° to 360°, depending on whether you're working with radians or degrees.
2. Plot the graph of sin(pi/2+Beta) on one set of axes and the graph of 1 + sinBeta on another set of axes.
3. On both graphs, mark the points where the two functions intersect. These points represent the values of Beta that satisfy the equation.
4. If the two graphs intersect at every point, regardless of the value of Beta, then the equation sin(pi/2+Beta) = 1 + sinBeta is an identity. This means the equation holds true for all values of Beta.
5. If the graphs do not intersect at every point, then the equation is not an identity. In this case, proceed to part (b) to find a value of Beta that makes the equation false.
To find a value of Beta that makes the equation false, look for a point where the graphs do not intersect. This means there is a value of Beta where sin(pi/2+Beta) is not equal to 1 + sinBeta. You can approximate the value of Beta by zooming in on the graph or by using numerical methods like solving equations or using a calculator.
By following these steps, you can use graphs to determine if the equation is an identity and find a value of the variable that makes the equation false if it is not.