What does it mean to find the value of #theta# that is a solution of the equation #4sin^3(2theta)=-1#?

1 Answer
Dwight · Shwetank Mauria
Mar 23, 2017

Here's what it means...(and the answer is #theta = -19.5^@#)

Explanation:

Treat the trigonometry function like any other variable, because that's what it is. We must perform a series of inverse operations - cube root and inverse sine to undo all these operations:

#4sin^3(2theta)=-1#

#sin^3(2theta)=-1/4#

Cube root of both sides:

#sin(2theta)=root(3)(-1/4)#

#sin(2theta)=-1/root(3)(4)#

Inverse sign

#2theta=sin^(-1)(-1/root(3)(4))#

The argument on the right is equal to #-39^@#

So, the final step is to divide both sides by #2#:

#theta =-19.5^@#

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1603 views around the world
You can reuse this answer
Creative Commons License