SOLUTION: Sir/Madam, How are you today,I am requesting you kindly to help me with 4 problems,I need to give positive values of the angle between 0degrees and 360degrees ,that will satisfy e

Question 321896: Sir/Madam,
How are you today,I am requesting you kindly to help me with 4 problems,I need to give positive values of the angle between 0degrees and 360degrees ,that will satisfy each and give approximate value to the nearest minutes.So far this is what i have tried: e.[sin(theta)=sqrt3/2] =[sin60dgrs=sqrt3/2]therefore,60dgrs and 120dgrs are the required value of(theta).f. (sin 2x=cos 2x)= (22 30',112 30',202 30,292 30')letter f,I have shown only the answer b'se of time. These are the 4 problems i need help with:
a.[sin(2x-10degrees)=1/2]; b.[cos 2x-sin^2(x/2+3/4)=0]; c.[sin^2(theta)=cos^(theta)+1/2]; d.[tan(x+15degrees)=3 tan x] P'se show work.Thanks much!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a. sin(2x-10degrees)=1/2
(2x - 10) = 30, 150, 390, 510 degs
2x = 40, 160, 400, 520�
x = 20, 80, 200, 260�
--------------------------
b. cos 2x-sin^2(x/2+3/4)=0
cos(2x) = 1 - 2sin^2(x)
1-sin^2(x) - sin^2(x/2 + 3/4) = 0
sin^2(x) + sin^2(x/2 + 3/4) = 1
Is there a typo?
-------------------
c. sin^2(theta)=cos^(theta)+1/2
Is that cos^2 ?? If so,
cos^2(t) - sin^2(t) = -1/2
cos(2t) = -1/2
2t = 120, 240, 480, 600�
theta = 60, 120, 240, 300�
----------------------------
d tan(x+15degrees)=3 tan x
(tan(x) + tan(15))/(1 - tan(x)*tan(15)) = 3tan(x)
tan(x) + tan(15) = 3tan(x) - 3tan^2(x)*tan(15)
3tan(15)*tan^2(x) - 2tan(x) + tan(15) = 0
tan(15) = tan(30/2) = sin(30)/(1+cos(30)) = (1/2)/(1 + sqrt(3)/2)
tan(15�) = 1/(2 + sqrt(3)) = 2 - sqrt(3)
-----------------------------------------
3tan(15)*tan^2(x) - 2tan(x) + tan(15) = 0 is a quadratic in tan(x).

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3.13843876330611 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.34594470271034, 0.142089169002246. Here's your graph:

=====================================
tan(x) = 0.142089169
x =~ 8.132 degs
-----------------
tan(x) = 2.3459447027
x =~ 66.913 degs

RELATED QUESTIONS
Dear Sir/Madam; Kindly help me with this problem, I am not familiar with this type... (answered by MathTherapy)

Dear Sir/Madam, I am confronted with the following problem: "T varies directly as... (answered by longjonsilver)

Dear Sir/Madam, I am confronted with the following problem: "Give polar coordinates... (answered by longjonsilver)

DEar Sir/Madam, Please help me in solving this problem, I am not much familiar with... (answered by solver91311)

Sir/Madam; A pleasant day! Kindly help me with this word problem about Law of... (answered by rothauserc)

Hello Sir/Madam I am having problems with my math and was wondering if you can provide (answered by ewatrrr)

I am having some trouble answering these question. Could someone kindly help me. 1.... (answered by tutorcecilia)

Dear Sir/Madam, I am confronted with the following problem: "Find the center and... (answered by rapaljer)

A pleasant day to you Sir / Madam, please do help me with this direct square variation (answered by Jolliano)