Main content

Get ready for AP® Calculus

Course: Get ready for AP® Calculus > Unit 7

Lesson 4: Sinusoidal equations

Solve sinusoidal equations (basic)

You might need: Calculator

Jamie tried to solve the following equation, where x is in radians to the nearest hundredth, in the interval from minus, pi to pi, but she made a mistake.

cosine, left parenthesis, x, right parenthesis, equals, minus, 0, point, 08

Here is Jamie's work.

\begin{array}{rcl} \cos^{-1}(\cos (x)) &= &\cos^{-1}( -0.08 )\\\\ x &\approx & 1.65\\\\ \swarrow&&\searrow\\\\ \begin{aligned} &\blueE{\text{Using }\cos(x)=\cos(x+2\pi)}\\\\ x &\approx 1.65+ 2\pi n\\\\ x &\approx \ldots -4.63\text{, }1.65\text{, }7.93\ldots \end{aligned}&& \begin{aligned} &\purpleD{\text{Using }\cos(x)=\cos(\pi-x)}\\\\ &\purpleD{\text{and }\cos(x)=\cos(x+2\pi)}\\\\ x &\approx 1.49 + 2\pi n\\\\ x &\approx \ldots -4.79\text{, }1.49\text{, }7.77\ldots \end{aligned} \end{array}

The solutions to x in the interval from minus, pi to pi are x, approximately equals, 1, point, 49 and x, approximately equals, 1, point, 65.

What was Jamie's mistake?

(Choice A)
Jamie evaluated cosine, start superscript, minus, 1, end superscript, left parenthesis, minus, 0, point, 08, right parenthesis in degrees instead of in radians.
(Choice B)
Jamie used an identity that only applies to the sine function, not to the cosine function.
(Choice C)
Jamie forgot to use negative n-values which would reveal more solutions in the interval.
(Choice D)
Jamie gave solutions that were outside of the interval.

Stuck?

Get ready for AP® Calculus

Course: Get ready for AP® Calculus > Unit 7

Problem