2Sin(Θ+47°)=1 ΘЄ[0°, 360°)
What I did:
Sin(Θ+47°)=1/2
Sin 1/2 = Θ+47°
30°+360 = Θ+47°
343° = Θ
Ok, so how do i find the other solutions? In this problem its 103°. I think we were suppose to do something with the graphing calculator and something about calculating the zero. I know how to do that, but i don't know how to make it equal 0 so i could put it in Y1? Any other way, what did i do wrong? Is there a prgm that is avilable for the Ti-83+ that can do these problems?
btw:
Θ = theta
Thanks in advance.
whtis the value of 343... figure that out .. and thn u can say that other solutions with be 2 pie ( n)
n wht ever value u figure out in radioans..
That looks like an equation, not an identity. If it were an identity, it would be true for all theta.
I am confused about what your symbol on the right side,
1 ΘЄ[0°, 360°)
is supposed to mean
Are you solving 2 Sin(Θ+47°)= 1 ?
If so, Sin(Θ+47°)=0.5
Θ+47° = 30, 150 or 390 degrees
Θ = 103 or 333 degrees if you are limited to theta between 0 and 360 degrees
the ΘЄ[0°, 360°) was suppose to mean its 0° < or = Θ < 360°
I get this now!!, Thanks!!!, i guess i should study now.
To find the other solutions for the equation 2Sin(Θ+47°) = 1, you can follow a similar approach as you did to find the first solution. However, instead of using 1/2 as the value for Sin(Θ+47°), you will use its complement, which is -1/2. This is because sine is positive in both the first and second quadrants.
Here's how you can find the other solution:
1. Sin(Θ+47°) = -1/2
2. From the unit circle or inverse sine function, you can determine that the reference angle whose sine value is -1/2 is 210°.
3. Subtracting 47° from 210° will give you the value of the angle without the +47° shift, which is 163°.
4. To find the other solution, add 360° to 163° since the angle needs to be within the range [0°, 360°].
5. The second solution is Θ = 163° + 360° = 523°.
So the solutions for the equation 2Sin(Θ+47°) = 1 are Θ = 343° and Θ = 523°.
As for using a graphing calculator like the TI-83+, you can plot the graph of the equation Y1 = 2Sin(θ+47°) - 1 and find the x-intercepts (values of θ) where the graph touches the x-axis. To calculate the zeros, you can use the "zero" or "root" function on the calculator. However, in this specific case, it might be easier and quicker to solve it algebraically as illustrated above.
Please note that I am not aware of any specific program (prgm) available for the TI-83+ that can directly solve trigonometric equations like this. However, there might be programs or apps created by other users that could help with such calculations. You can explore online resources or calculator forums to find programs compatible with your calculator that may assist with solving trigonometric equations.