Jace K. answered • 02/15/22
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Former Calculus Teacher
Let "log3" be "log" for this answer. log(x^9) = 9log(x), so we can rewrite the expression on the left as: log(x) + 27log(x) = 28log(x). From here, divide both sides by 28 and then exponentiate both sides:
log(x) = 17/28
x = 3^(17/28)
Jace K.
sin(pi/3) = sqrt(3)/2, and sin(4pi/3) = -sqrt(3)/2. Then, asking what sin^-1(x) is asking "what angle will give me this x-value if I take the sine of the angle". For sqrt(3)/2, we already know the angle must be pi/3, since that's the angle we started with that gave us sqrt(3)/2 when we took the sine of it. cos^-1 is the same question but with cosine. So what angle gives -sqrt(3)/2 if we take the cosine of it? If you looked at a unit circle, you'd see that that angle is 5pi/6. From there, you should be able to plug in and compute: f(pi/3) = 3 * pi/3 + 4 * 5pi/6 Simplify and you're done!
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02/15/22
Anjela R.
Thank you, I appreciate it
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02/15/22
Anjela R.
Can you please help me with this question Determine the value of 𝑓(𝑥)=3sin^−1(sin(𝑥))+4cos^−1(sin(4𝑥)) at 𝑥 =𝜋/3 (Use symbolic notation and fractions where needed.)02/15/22