nickb145 said:Homework Statement
i have
solve 7sin(2x)-13sin(x)=0
for all solutions 0≤X<2p
I used the double angle formula for sin(2x)=2sin(x)cos(x)
The Attempt at a Solution
I'm getting stuck near the end
7(2sin(x)cos(x)-13sin(x))
14sin(x)cos(x)-13sin(x)
now I am stuck
Curious3141 said:What you wrote aren't equations. An equation must have two sides separated by an '='. In this case, your right hand side (RHS) equals 0.
In that final equation, can you find a common factor between the two terms?
Finding all solutions of sin on the interval means finding every possible value for the sine function within a given interval. This can be done by using mathematical techniques such as graphing or solving equations.
It is important to find all solutions of sin on the interval in order to fully understand the behavior of the sine function and to accurately solve trigonometric equations involving sine.
The interval refers to a specific range of values for the independent variable (typically represented by x) in a given function. In this case, it is the range of values for which we are finding solutions for the sine function.
Some common methods for finding all solutions of sin on the interval include graphing, using trigonometric identities, and solving equations using algebraic techniques. The specific method used will depend on the given problem and the level of accuracy required.
Yes, there can be an infinite number of solutions for sin on the interval. This is because the sine function is a periodic function, meaning it repeats itself infinitely. Therefore, there will always be an infinite number of solutions within any given interval.