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ACT Math : Trigonometry

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Example Questions

Example Question #51 : Trigonometry

What is the reference angle for $257^{\circ}$ ?

Possible Answers:

$77^{\circ}$

$257^{\circ}$

$103^{\circ}$

$13^{\circ}$

$93^{\circ}$

Correct answer:

$77^{\circ}$

Explanation:

A reference angle is the smallest possible angle between a given angle measurement and the x-axis.

In this case, our angle $257^{\circ}$ lies in Quadrant III, so the angle is found by the formula $\angle A_r = \angle A - 180^{\circ}$ .

$\angle A_r = \angle A - 180^{\circ}$ $257^{\circ} - 180^{\circ} = 77^{\circ}$

Thus, the reference angle for $257^{\circ}$ is $77^{\circ}$ .

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Example Question #51 : Trigonometry

What is the reference angle for $125^{\circ}$ ?

Possible Answers:

$55^{\circ}$

$35^{\circ}$

$125^{\circ}$

$75^{\circ}$

$235^{\circ}$

Correct answer:

$55^{\circ}$

Explanation:

A reference angle is the smallest possible angle between a given angle measurement and the x-axis.

In this case, our angle $125^{\circ}$ lies in Quadrant II, so we can find our reference angle using the formula

$\angle A_r = 180^{\circ}- \angle A$ .

$\angle A_r = 180^{\circ}- \angle A$ $180^{\circ} - 125^{\circ} = 55^{\circ}$

Thus, the reference angle for $125^{\circ}$ is $55^{\circ}$ .

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Example Question #1 : How To Find The Period Of The Sine

What is the period of 2sin(4Θ)?

Possible Answers:

None of the answers are correct

$2\pi$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

The period of sinΘ is 2Π, so we set the new angle equal to the base period of 2Π and solve for Θ.

So 4Θ = 2Π and Θ = Π/2.

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Example Question #1 : How To Find The Period Of The Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of

$sin\, (\pi x)$ .

Possible Answers:

$4\pi$

$2\pi$

$\pi$

Correct answer:

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

$\frac{2\pi}{A}$

in this case

$\frac{2\pi}{\pi}$

which reduces to .

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Example Question #1 : Sine

A function with period P will repeat on intervals of length P, and these intervals are referred to as periods.

Find the period of the function

$\sin \bigg(\frac{1}{2}x\bigg)$ .

Possible Answers:

$\frac{1}{2}$

$4\pi$

$\pi$

Correct answer:

$4\pi$

Explanation:

For the function

$sin\, (Ax)$

the period is equal to

$\frac{2\pi}{A}$

in this case

$\frac{2\pi}{\frac{1}{2}}=2\pi \cdot \frac{2}{1}$

which reduces to $4\pi$ .

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Example Question #3 : How To Find The Period Of The Sine

What is the period of the function $f(t) = -2\sin(4t)$ ?

Possible Answers:

$2\pi$

$-\pi$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To find the period of Sine and Cosine functions you use the formula:
$\frac{2\pi}{\left | b\right |}$ where comes from $f(t) = a\sin(bt)$ . Looking at our formula you see b is 4 so
$\frac{2\pi}{\left | 4\right |}=\frac{\pi}{2}$

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Example Question #52 : Trigonometry

What is the period of the given trigonometric function:

$c(t) = 3\sin(-2t)$ . Leave your answer in terms of $\pi$ , simplify all fractions.

Possible Answers:

$-\pi$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\pi$

$-\frac{\pi}{2}$

Correct answer:

$\pi$

Explanation:

To find the period of a sine, cosine, cosecant, or secant funciton use the formula:

$\omega = \frac{2\pi}{\left|b\right|}$ where comes from the general formula: $c(t)=a\sin(bt)$ . We see that for our equation $\left|b\right| = 2$ and so the period is $\pi$ when you reduce the fraction.

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Example Question #1 : Sine

Find the period of the following formula:

$f(x)=2\sin(4\theta)$

Possible Answers:

$\frac{\pi}{2}$

$\frac{1}{\pi}$

$2\pi$

$\pi$

$\frac{2}{\pi}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To find period, simply remember the following formula:

$\textup{period}=\frac{2\pi}{B}$

where B is the coefficient in front of x. Thus,

$\textup{period}=\frac{2\pi}{4}=\frac{\pi}{2}$

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Example Question #1 : How To Find The Domain Of The Sine

Find the domain of the function: $y=-9\sin(5\theta-3)-3$

Possible Answers:

$\left(-\frac{2\pi}{5},\infty\right)$

$\left(-\frac{2\pi}{5},\frac{2\pi}{5}\right)$

${}(-\infty,\infty)$

$\left[-\frac{2\pi}{5},\frac{2\pi}{5}\right]$

$\left(-\frac{5}{3},\frac{2\pi}{5}\right)$

Correct answer:

${}(-\infty,\infty)$

Explanation:

The function $y=-9\sin(5\theta-3)-3$ is related to the parent function $y=\sin(\theta)$ , which has a domain of $(-\infty.\infty)$ .

The value of theta for $y=-9\sin(5\theta-3)-3$ has no restriction and is valid for all real numbers.

The answer is $(-\infty,\infty)$ .

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Example Question #2 : Sine

What is the domain of the given trigonometric function:

$z(t) = 2\sin(-2t)$

Possible Answers:

$[0,\infty]$

$[-\pi,\pi]$

[-2,2]

$(-\infty,\infty)$

[-2,0]

Correct answer:

$(-\infty,\infty)$

Explanation:

For both Sine and Cosine, since there are no asymptotes like Tangent and Cotangent functions, the function can take in any value for . Thus the domain is:

$(-\infty,\infty)$

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ACT Math : Trigonometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #51 : Trigonometry

Example Question #51 : Trigonometry

Example Question #1 : How To Find The Period Of The Sine

Example Question #1 : How To Find The Period Of The Sine

Example Question #1 : Sine

Example Question #3 : How To Find The Period Of The Sine

Example Question #52 : Trigonometry

Example Question #1 : Sine

Example Question #1 : How To Find The Domain Of The Sine

Example Question #2 : Sine

All ACT Math Resources

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