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17. Use the Addition Formula to prove that gin(T + 0) = sin 0.18. Rewrite the expression gin(arctan z) in termg of €....

Question

17. Use the Addition Formula to prove that gin(T + 0) = sin 0.18. Rewrite the expression gin(arctan z) in termg of €.

17. Use the Addition Formula to prove that gin(T + 0) = sin 0. 18. Rewrite the expression gin(arctan z) in termg of €.



Answers

In Exercises 19–22, find the product of z1 and z2. Leave the answer in trigonometric form.
$$
\begin{array}{l}{z_{1}=\sqrt{2}\left(\cos 118^{\circ}+i \sin 118^{\circ}\right)} \\ {z_{2}=0.5\left[\cos \left(-19^{\circ}\right)+i \sin \left(-19^{\circ}\right)\right]}\end{array}
$$

Okay, So how can I rewrite this? Well, persons figure, is it signed Cozaar Tangent? Well, two straight. It's all in the numerator, so it doesn't have a fraction. So it's gonna be center Co sign. And since signing co sign are multiplied together, I know it's gonna be signed because co sign the formulas have co sign Multiply together. Island sidles together for sign. It's definitely gonna be We keep the same operation addition and then my two angles Air 18 and 27. Let's just vilify this. 18 plus 27 is just 45 degrees. What sign of 45 degrees we're to over to will be my answer.

So we need to show that if Z is equal to co sign of data plus, I sine of data in the absolute value of Z is equal to one. So remember that Z is written in the form of X plus I Y. And the absolute value of Z is equal to our which is equal to the square root of X squared plus y squared. So we have that this is equal to the square root of close in squared of data plus sine squared of data. So this is a trick identity that is equal toe one. So we have that this is equal to square root of one which is equal one. So if Z is equal to co sign if data plus i sine of data, the absolute value of Z is equal to one.

So we can solve for this quotient Here. See? One divided by sea to buy first dividing our co efficient. So we have 22 divided by 11 which gives us a value of two. So we have two times co sign and our angle here for this coastline is 11 pi over 18 minus 55 or 18. So 11 minus five gives us a value of six. And so 65 18 can be rewritten as pi over three. So you have coastline of firing three. Plus I sign of, however three. And so we know that co sign of private three is 1/2. So we have two times 1/2 plus Route 3/2 I. And so our solution here is one plus Route three. Hi. So this is our solution.

We have a London first one under Sivan 17 And of it it is given that, if so, that it will toe general far too. Then to show that sign, I'll fight equal to Does that over one place? Xander Square. So if you remember a formula signed rotator equal to dude Anteater Oh, one place 10 square teeter. And if we we'll plug in Tetovo to in my in place of Tater you're getting scientific tickle toe do then teeter were too over one place 10 square feet over to here. It it just Jennifer in place off. We have Sino for we can bet. Ah, this good bait. And as to Dannell forward to over one plus 10 square. And if I were to now we have tell from a trickle to is dead, so d should bitterness sign off. I call to who was it? Well, uh, one place I was there. Just square. So this is, uh, roomed are This was rubbish on and we have shown that Thank you so much.


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