Question

3. Find all solutions to the equation 3cos(3x) = −7/5 without a calculator

Answer 1

Answer:

x = 1/3 (arccos (-7/15) + 2πn)

Explanation:

For solving for x in

$3\cos \mleft(3x\mright)=-\frac{7}{5}$

we first divide both sides by 3 to get

$\cos (3x)=-\frac{7}{3\times5}$$\cos (3x)=-\frac{7}{15}$

taking the arccos of both sides gives

$\arccos \lbrack\cos 3x\rbrack=\arccos (-\frac{7}{15})$$3x=\arccos (-\frac{7}{15})+2\pi n$

finally, dividing both sides by 3 gives

$\boxed{x=\frac{1}{3}\lbrack\arccos (-\frac{7}{15})+2\pi n\rbrack}$

where n is an integer.

We can find the numerical answer for x by using a calculator to find the value of arccos(-7/15).