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ACT Math : ACT Math

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Example Questions

Example Question #2961 : Act Math

Simplify the following expression:

$\frac{sin\theta}{cot\theta sec\theta}$

Possible Answers:

tanΘ

None of the answers are correct

cscΘ

sin²Θ

cos²Θ

Correct answer:

sin²Θ

Explanation:

Convert cotΘ and secΘ to sinΘ and cosΘ and simplify the resulting complex fraction.

cotΘ = cosΘ secΘ = 1

sinΘ cosΘ

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Example Question #2962 : Act Math

What is the reference angle for $855^{\circ}$ ?

Possible Answers:

$495^{\circ}$

$720^{\circ}$

$45^{\circ}$

$360^{\circ}$

$55^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

The reference angle is between 0^o and $90^{\circ}$ , starting on the positive -axis and rotating in a counter-clockwise manor.

To find the reference angle, we subtract 360^o for each complete revolution until we get a positive number less than 360^o .

855 - 360 = 495

495 - 360 = 135

855^o is equal to two complete revolutions, plus a $135^{\circ}$ angle. Since $135^{\circ}$ is in Quadrant II, we subtract it from $180^{\circ}$ to get our reference angle:

$180-135=45^{\circ}$

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Example Question #2963 : Act Math

Unit_circle

In the unit circle above, if $\Theta =30^{\circ}$ , what are the coordinates of (X,Y) ?

Possible Answers:

$\left (\frac{1}{2},\frac{\sqrt{3}}{2} \right )$

$\left (\frac{1}{2},\frac{1}{2} \right )$

$\left (1,\frac{1}{2} \right )$

$\left (\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2} \right )$

$\left (\frac{\sqrt{3}}{2},\frac{1}{2} \right )$

Correct answer:

$\left (\frac{\sqrt{3}}{2},\frac{1}{2} \right )$

Explanation:

On the unit circle, (X,Y) = (cos Θ, sin Θ).

(cos Θ,sin Θ) = (cos 30º, sin 30º) = (√3 / 2 , 1 / 2)

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Example Question #44 : Trigonometry

What is the reference angle for $45^{\circ}$ ?

Possible Answers:

$180^{\circ}$

$45^{\circ}$

$135^{\circ}$

$315^{\circ}$

$90^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

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

In this case, our angle $45^{\circ}$ lies in Quadrant I, so the angle is its own reference angle.

Thus, the reference angle for $45^{\circ}$ is $45^{\circ}$ .

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Example Question #51 : Trigonometry

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

Possible Answers:

$103^{\circ}$

$13^{\circ}$

$77^{\circ}$

$93^{\circ}$

$257^{\circ}$

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 #52 : Trigonometry

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

Possible Answers:

$35^{\circ}$

$235^{\circ}$

$75^{\circ}$

$125^{\circ}$

$55^{\circ}$

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 : Sine

What is the period of 2sin(4Θ)?

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

None of the answers are correct

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 #2964 : Act Math

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:

$\pi$

$\frac{1}{2}$

$4\pi$

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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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2961 : Act Math

Example Question #2962 : Act Math

Example Question #2963 : Act Math

Example Question #44 : Trigonometry

Example Question #51 : Trigonometry

Example Question #52 : Trigonometry

Example Question #1 : Sine

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

Example Question #2964 : Act Math

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

All ACT Math Resources

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