Solve 6 sin ( x/2)= 1 on [-20,30], Mathematics

Solve 6 sin ( x/2)= 1 on [-20,30]

Solution

Let's first work out calculator of the way since that isn't where the difference comes into play.

sin( x/2)= 1/6   ⇒x/2= sin -1( 1/6)= 0.1674

Here's a unit circle for this instance.

246_circle29.png

To determine the second angle in this case we can notice that the line in the first quadrant makes an angle of 0.1674 with the +ve x-axis and hence the angle in the second quadrant will then make an angle of 0.1674 with the -ve x-axis and hence the angle that we're after is then,

π - 0.1674 =2.9742 .

Here's the rest of the solution for this instance.  We're going to assume from this point on that you can do this work without much explanation.

x/2= 0.1674  + 2π n  ⇒         x = 0.3348 + 4π n          n= 0, ±1, ±2,.......

x/2= 2.9742 ± 2π nx = 5.9484 ± 4π n

n= -2 :x =  -24.7980 and   -19.1844

n = -1 :x = -12.2316  and  -6.6180

n = 0    : x = 0.3348    and      5.9484

n = 1    : x =12.9012    and      18.5148

n = 2    :x = 25.4676   and      31.0812

The solutions to this equation are then,

 x = -19.1844, -12.2316, - 6.6180, 0.3348, 5.9484, 12.9012, 18.5128, 25.4676

Note that in the previous instance we only got a single solution. It happens on occasion thus don't get worried regarding it. Also, note that it was the second angle which gave this solution and hence if we'd just relied on our calculator without worrying regarding other angles we would not have gotten this solution.  Again, it can't be stressed sufficient that whereas calculators are a great tool if we don't understand how to properly interpret/use the result we can (and frequently will) get the solution wrong.

To this point we've only worked examples including sine & cosine. Nowlet's work a couple of instance that involves other trig functions to see how they work.

Posted Date: 4/11/2013 2:41:02 AM | Location : United States







Related Discussions:- Solve 6 sin ( x/2)= 1 on [-20,30], Assignment Help, Ask Question on Solve 6 sin ( x/2)= 1 on [-20,30], Get Answer, Expert's Help, Solve 6 sin ( x/2)= 1 on [-20,30] Discussions

Write discussion on Solve 6 sin ( x/2)= 1 on [-20,30]
Your posts are moderated
Related Questions
My thousandths digit is twice the tenths digit. My tenths digit is one less than the hundredths digit. If my number is 5, what my number?

the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?

how to solve the equation of an inverse function

If there are (2n+1)terms  in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n Ans:    Let a, d be the I term & Cd of the AP. ∴ ak =

class 10 Q.trigonometric formula of 1 term

. The Boeing Company makes a number of different types of aircraft for the commercial airline industry, e.g., the 727, 747, 757, 767, and 777 jet models. Is there any way for Boei

Equal-sharing - situations in which we need to find out how much each portion Multiplication and Division contains when a given quantity is shared out into a number of equal porti

INTRODUCTION :  Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this

Forecasting By Using Least Squares Data have been kept of sales over the last seven years Year 1 2 3 4 5 6

if two circles O and O''intersect in two points, A and B, the the line segment OO is what?