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SAT II Math II : Solving Trigonometric Functions

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Example Questions

Example Question #1 : Solving Trigonometric Functions

Give the period of the graph of the equation

$f(x) = \frac{2}{9} \sin 8 x$ $\displaystyle f(x) = \frac{2}{9} \sin 8 x$

Possible Answers:

The correct answer is not among the other choices.

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{9}{2}$ $\displaystyle \frac{9}{2}$

$\displaystyle 8$

Correct answer:

The correct answer is not among the other choices.

Explanation:

The period of the graph of a sine function $f(x)= A \sin Bx$ $\displaystyle f(x)= A \sin Bx$ is $\frac{2 \pi}{B}$ $\displaystyle \frac{2 \pi}{B}$ , or $2 \pi \div B$ $\displaystyle 2 \pi \div B$ .

Since B= 8 $\displaystyle B= 8$ ,

$2 \pi \div 8 = \frac{\pi }{4}$ $\displaystyle 2 \pi \div 8 = \frac{\pi }{4}$ .

This answer is not among the given choices.

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Example Question #2 : Solving Trigonometric Functions

If $\displaystyle f(x)=2sin(x)+cos(x)$ , what must $f(\frac{\pi}{4})$ $\displaystyle f(\frac{\pi}{4})$ be?

Possible Answers:

$3\sqrt{2}$ $\displaystyle 3\sqrt{2}$

$4\sqrt2$ $\displaystyle 4\sqrt2$

$\textup{The answer is not given.}$ $\displaystyle \textup{The answer is not given.}$

$\frac{\sqrt2}{2}+2$ $\displaystyle \frac{\sqrt2}{2}+2$

$\frac{3\sqrt2}{2}$ $\displaystyle \frac{3\sqrt2}{2}$

Correct answer:

$\frac{3\sqrt2}{2}$ $\displaystyle \frac{3\sqrt2}{2}$

Explanation:

Evaluate each trig function at the specified angle.

$sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\displaystyle sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$

$cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\displaystyle cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$

Replace the terms into the function.

$f(\frac{\pi}{4})=2sin(\frac{\pi}{4})+cos(\frac{\pi}{4}) = 2(\frac{\sqrt{2}}{2})+\frac{\sqrt{2}}{2}$ $\displaystyle f(\frac{\pi}{4})=2sin(\frac{\pi}{4})+cos(\frac{\pi}{4}) = 2(\frac{\sqrt{2}}{2})+\frac{\sqrt{2}}{2}$

Combine like-terms.

The answer is: $\frac{3\sqrt2}{2}$ $\displaystyle \frac{3\sqrt2}{2}$

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SAT II Math II : Solving Trigonometric Functions

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Solving Trigonometric Functions

Example Question #2 : Solving Trigonometric Functions

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