Solve each equation for x, where x is restricted to the given ...

Question

Solve each equation for x, where x is restricted to the given interval.

y = ― 2 cos 5x , for x in [0, π/5]

Accepted Answer

About the ball, we equation for X if X slides in the interval from zero to pi divided by eight with our equation, it's Y equals negative four cosine A X and we have four possible answers. X equals 18, assigned inverse Y divided by four, X equals eight Poseidon. Verse Y divided by four, X equals eight cosine inverse negative four Y and X equals 1/8 cosine and verse negative Y divided by four. Now for this problem, I'll first rewrite our equation to have X on the left side, you can write this as naked with four cosine eight X equals Why? Now we have to solve for X X is actually inside of the coast on function. So we first seem to get rid of our negative poor negative force of cosine. So it kind of has to go first, let's get rid of it by dividing both sides by negative four. We end up getting O sine eight X equals negative Y divided by four. Now we have to solve for eggs still. So we can now get rid of the cosine function. Let's take the inverse cosine on both sides. The inverse cosine and cosine will cancel each other out. Giving us eight X equals cosine inverse negative Y divided by four. Finally, we can divide both sides by eight ticket X equals cosine inverse negative Y divided by four all divided by eight, which finally simplifies to X equals 1/8 cosine and verse negative Y divided by four. We don't have any more simplification to do Bush makes the answer to our problem. Answer the OK. Hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each equation for x, where x is restricted to the given interval.
y = ― 2 cos 5x , for x in [0, π/5]

Key Concepts

Solving Trigonometric Equations

Properties of the Cosine Function

Interval Restrictions and Domain Considerations

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