Solution
Solution
+1
Radians
Solution steps
Rewrite using trig identities:
Use the following identity:
Simplify:
Least Common Multiplier of
Least Common Multiplier (LCM)
Prime factorization of
is a prime number, therefore no factorization is possible
Prime factorization of
is a prime number, therefore no factorization is possible
Multiply each factor the greatest number of times it occurs in either or
Multiply the numbers:
Adjust Fractions based on the LCM
Multiply each numerator by the same amount needed to multiply its
corresponding denominator to turn it into the LCM
For multiply the denominator and numerator by
For multiply the denominator and numerator by
Since the denominators are equal, combine the fractions:
Add similar elements:
Rewrite using trig identities:
Write as
Use the Half Angle identity:
Use the Double Angle identity
Substitute with
Switch sides
Divide both sides by
Square root both sides
Choose the root sign according to the quadrant of :
Rewrite using trig identities:
Show that:
Use the following product to sum identity:
Show that:
Use the Double Angle identity:
Divide both sides by
Use the following identity:
Divide both sides by
Divide both sides by
Substitute
Show that:
Use the factorization rule:
Refine
Show that:
Use the Double Angle identity:
Divide both sides by
Use the following identity:
Divide both sides by
Divide both sides by
Substitute
Substitute
Refine
Add to both sides
Refine
Take the square root of both sides
cannot be negativecannot be negative
Add the following equations
Refine
Simplify
Join
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Multiply the numbers:
Add the numbers:
Apply the fraction rule:
Multiply the numbers:
Apply radical rule: assuming
Prime factorization of
divides by
divides by
is a prime number, therefore no further factorization is possible
Apply exponent rule:
Apply radical rule:
Apply radical rule:
Rationalize
Multiply by the conjugate
Apply exponent rule:
Add similar elements:
Multiply fractions:
Cancel the common factor:
Add the numbers:
Cross multiply
Apply fraction cross multiply: if then
Simplify
Multiply fractions:
Cancel the common factor:
Switch sides
Divide both sides by
Divide both sides by
Simplify
Simplify
Divide the numbers:
Simplify
Apply the fraction rule:
Multiply the numbers:
Verify Solutions
Find undefined (singularity) points:
Take the denominator(s) of and compare to zero
The following points are undefined
Combine undefined points with solutions:
Apply trig inverse properties
General solutions for
Show solutions in decimal form
Popular Examples
sin(x)-sqrt(3)cos(x)=1,0<= x<2pisin(α)+1=cos(α)(sin(115))/(53)=(sin(S))/(83)2cos(x)-tan(x)=00=3sin(x)
Frequently Asked Questions (FAQ)
What is the general solution for (10)/(sin(x))=(13)/(sin(72)) ?
The general solution for (10)/(sin(x))=(13)/(sin(72)) is x=0.82063…+360n,x=180-0.82063…+360n