5

[30]=- sin(2x 41) V = 3 sin(4x Sketch the graph ofandsin(xwithin O<x < 2tt...

Question

[30]=- sin(2x 41) V = 3 sin(4x Sketch the graph ofandsin(xwithin O<x < 2tt

[30] =- sin(2x 41) V = 3 sin(4x Sketch the graph of and sin(x within O<x < 2tt



Answers

35-40 Find $\sin \frac{x}{2}, \cos \frac{x}{2},$ and $\tan \frac{x}{2}$ from the given information.
$\sec x=\frac{3}{2}, \quad 270^{\circ} < x < 360^{\circ}$

Me a problem. But 35 35 investigated to find sine X by two Because exploit toe and 10 x right to sign experts because expert duty next way to from the given information. So sign axes given as three by five Where zero degree Listen. Actually then 90 degree. So this isn't first quarter and so all their issues will be positive. Okay, so from Brighton aren TT you will be having cost X equal to one minus science Quad X and the route one minus three of our five whole squad in the route that is one minus nine y 25 which is 60 million different on four by fight. So we have course X equal toe for by five. Now we'll be starting. Our problem are a sine x by two So we're going toe Ah, half angle identity. It will be one minus cause you by two on the route not cost you. It will because sex because we're using x Okay, cause X Y two no sign next by two will be equal to one minus. We have found a very of course X as four by five divided by two of fireman's for one by 10. So saying expert two is equal to one by 10. And, um, if they just multiply and divide by 10 we will be getting sine X y to equal to under a 10 by 10. This is sign Expecto part B. It's cause expert too. Course X by toe that is one place cause x by two about a lasting 1/2 angry Formula One. Place for my fire by two 85. Plus for nine by 10 in the road three by under 10. Multiply and divide by under. Then people were getting course exploit to equal toe. Three under 10 by 10 Now comes part C, which is 10 x by two it will be Quito one of minus cause x by sine x So one miners four by five by five So five minutes for one by five in 25 by three. 13 x y two is one month three One more three. Thank you so much

We want to solve this equation and we can vital function as coastlines reacts our nurse. Let's all relax plus cynics and hence we want to find acts such as the function value is Greater than or equal to zero. This is a growth of the functioning of the arts. And we can say that It intersects with the X. Axis are three points and we just rooming this free injured. And we can see for the first intercept. It is approximately point fix it. For the second intersection. It is approximately one point train north and for the third intersection The point is two points fire three enhance the solution for this. You creating uh from 0 2.66 and then from one point 3922.53.

In this problem. But given aggression can we read it in us Ton of three x -1. divided by turn off three x plus one Is by dividing the numerator and denominator by course of three X. This has given us less than zero Case. one is that Then three x plus one is a positive value which means that Then three explainers, 1 is less than zero from here. We understand that 10 3 X Lies between -1- one. And the second case is that 10 3 X plus one is Less than zero and and three x -1 is greater than zero from first we get there 10 3 Xs less than minus one from second street. When we get there 10 3 X is greater than one. These two statements can never be occurring together. So we will omit this case. Now let us look at the graph of panel fix. This is this corresponds to bye bye to and this corresponds to minus spiral too. This is zero. This is ban of X. And this is X. Now this is the line corresponding to 10 x equals 2 -1. And this is the line corresponding to Turn off x equals to one. This point and this point are Bye Bye. four and minus my rifle which means that three X lies between -5 x 4 to five vessels. Looking at the situation which means that X lies between minus by vegetable too. By my 12. Now uniting the general solution since we know the period for tan a spy for 10 3. Exodus Bye Bye three. So empire by three minus By about 12 comma. And by by three plus. Bye bye. Right And belonging to 01. Doing so.

We want to solve the equation. Co Osan of three. It's Equals the son of 38 Gonna begin by dividing by coasts of the coasts on on both sides of the equation. The reason I wanted that it's because and the sand about tobacco sound is change it. It's all divided by co sign of 38 Seer and Alka Bad Co sign of three. It's here when I do that I have one equals The tangent of three. It's so now let's think about her unit circle and I'm not actually drawing the unit circle. I'm just drawing my special right triangles. Changin is positive in quadrant one and in quadrant three. Now tangent this Saad opposite oversight adjacent. So to make this one, we would have won over one in Quadrant three. The side opposite would be negative. One over negative one now in quadrant woolen. I know that my reference angle there is power forward. See, this is a 45 degree angle here. This special right, triangles 45 45 90 and in radiance, that would be power for four. So now when we solve that equation for its will have its equals. Have for 12. Dan in quadrant three, we have three X equals and this angle again, that reference angle is power forward. So to find the angle that is sweat. We have, uh, plus, however forward and so that would be five power over four. We're now when I divide by three, I'm going to have its equals. Faz, huh? Over 12. So the two angles.


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