Solving Trigonometric Functions

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SAT Math › Solving Trigonometric Functions

Questions 1 - 2

1

Give the period of the graph of the equation

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

The correct answer is not among the other choices.

$\frac{1}{8}$

$\frac{2}{9}$

$\frac{9}{2}$

Explanation

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

Since ,

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

This answer is not among the given choices.

2

If , what must $f(\frac{\pi}{4})$ be?

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

$3\sqrt{2}$

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

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

$4\sqrt2$

Explanation

Evaluate each trig function at the specified angle.

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

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

Replace the terms into the function.

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

Combine like-terms.

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

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