in Other Math Topics by Level 4 User (6.9k points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

We can write this: sin(90-(3x+28))=sin(2x+28).

So 90-3x-28=2x+28, 34=5x, x=6.8° is one solution.

But cos(3x+28)=cos(-3x-28)=sin(90+3x+28)=sin(2x+28), 90+3x=2x, x=-90°=270° is another solution.

And there are many solutions derived from these two, because cos(360+A)=cosA and sin(360+A)=sinA.

The easiest way to find all the solutions is to draw a graph of y=cos(3x+28) and y=sin(2x+28). You will see where the two curves intersect and you should spot a pattern that will enable you to write a general expression for all the solutions (e.g., 6.8, 78.8, 150.8, 222.8, 270, 294.8, 366.8, etc.).

Two general formulae for x in degrees are:

x=6.8+72n (derived from 5x=34+360n) and x=270+360n, where n is any integer, positive or negative.

by Top Rated User (659k points)

Related questions

2 answers
asked Mar 18, 2016 in Other Math Topics by Oscar Antonio Manuel Alvarez | 251 views
1 answer
2 answers
asked Apr 6, 2011 in Algebra 1 Answers by anonymous | 1.2k views
2 answers
asked Oct 29, 2013 in Fraction Problems by ezelliam | 129 views
1 answer
1 answer
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
83,149 questions
87,973 answers
4,851 users