Homework Statement
Calculate the number of moles and mass of BaCl2 and NaCl in the original mixture.
Homework Equations
We prepared a solution of 0.35M Na2SO4. We then obtained an unknown mixture of BaCl2•2H2O and NaCl, weighed 1 g and added it to 200 mL of water and 10 mL HCl. Finally we...
Alright. So if cos(90°-x)=sinx, which in my case is 70°, I still do not understand why Tanya then encourages me to use sin^-1(sinθ)=θ. How is cos70° to be replaced by sinθ? By the trig identities, sin(90°-x)=cosx, it is sin20° which is equivalent to cos70°. Would my equation then be accurately...
Homework Statement
d/dx(sec(x)/1+tan(x)
Evaluate at x=∏/6
Homework Equations
The Attempt at a Solution
((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2
((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))
I used the quotient rule and reduced what I could. Have I done this...
Finding sine and cosine of 390° or 30° is not difficult. Converting sin390°=0.5 into 1/2 is simple as well. However, when it comes to converting cos390°=0.866 into √3/2, I am at a loss.
I understand how to convert between radians and degrees. What I am unsure of is how to get from the radians to those fractions. When I write the exam, I am not allowed a scientific calculator either, so I definitely need to know this. Also, Sammy, while this may be basic to you, it is not...
Homework Statement
4{cos(13∏/6)+isin(13∏/6)}
= 4((√3/2)+(i/2))
= 2√3+2i
Homework Equations
The Attempt at a Solution
This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.
Homework Statement
Let T: R3 -> M22 by
T\begin{bmatrix}
a \\
b \\
c
\label{T}
\end{bmatrix}
=
\begin{bmatrix}
a-b & b-c \\
a+b & b+c\\
\end{bmatrix}
Is this transformation one-to-one?
Homework Equations
The Attempt at a Solution
I am not really certain...