Trigonometry - ACT Math
Card 1 of 56
What is $\sin\theta$ in a right triangle?
What is $\sin\theta$ in a right triangle?
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$\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$ (for an acute angle $\theta$ in the triangle)
$\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$ (for an acute angle $\theta$ in the triangle)
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If $\sin\theta = \dfrac{3}{5}$, what is $\csc\theta$?
If $\sin\theta = \dfrac{3}{5}$, what is $\csc\theta$?
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$\csc\theta = \dfrac{5}{3}$
$\csc\theta = \dfrac{5}{3}$
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What is $\cos 180°$?
What is $\cos 180°$?
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$-1$
$-1$
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In a right triangle, the side opposite angle $\theta$ is $7$ and the side adjacent is $24$. Find $\tan\theta$.
In a right triangle, the side opposite angle $\theta$ is $7$ and the side adjacent is $24$. Find $\tan\theta$.
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$\tan\theta = \dfrac{7}{24}$
$\tan\theta = \dfrac{7}{24}$
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What are the exact values of $\sin 45°$, $\cos 45°$, and $\tan 45°$?
What are the exact values of $\sin 45°$, $\cos 45°$, and $\tan 45°$?
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$\sin 45° = \dfrac{\sqrt{2}}{2}$, $\cos 45° = \dfrac{\sqrt{2}}{2}$, $\tan 45° = 1$
$\sin 45° = \dfrac{\sqrt{2}}{2}$, $\cos 45° = \dfrac{\sqrt{2}}{2}$, $\tan 45° = 1$
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Convert $90°$ to radians.
Convert $90°$ to radians.
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$\dfrac{\pi}{2}$ ($90 \times \dfrac{\pi}{180} = \dfrac{\pi}{2}$)
$\dfrac{\pi}{2}$ ($90 \times \dfrac{\pi}{180} = \dfrac{\pi}{2}$)
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What is $\tan 90°$?
What is $\tan 90°$?
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Undefined
Undefined
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In a right triangle with hypotenuse $10$ and one angle $30°$, find the side opposite the $30°$ angle.
In a right triangle with hypotenuse $10$ and one angle $30°$, find the side opposite the $30°$ angle.
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$5$ (Use $\sin 30° = \dfrac{\text{opp}}{10} \Rightarrow \dfrac{1}{2} = \dfrac{\text{opp}}{10} \Rightarrow \text{opp} = 5$)
$5$ (Use $\sin 30° = \dfrac{\text{opp}}{10} \Rightarrow \dfrac{1}{2} = \dfrac{\text{opp}}{10} \Rightarrow \text{opp} = 5$)
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What is the Pythagorean identity for sine and cosine?
What is the Pythagorean identity for sine and cosine?
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$\sin^2\theta + \cos^2\theta = 1$
$\sin^2\theta + \cos^2\theta = 1$
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What is $\cos 90°$?
What is $\cos 90°$?
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$0$
$0$
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How do you convert radians to degrees?
How do you convert radians to degrees?
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Multiply by $\dfrac{180}{\pi}$, or use: degrees $= \text{radians} \times \dfrac{180}{\pi}$
Multiply by $\dfrac{180}{\pi}$, or use: degrees $= \text{radians} \times \dfrac{180}{\pi}$
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If $\sin\theta = -\dfrac{3}{5}$ and $\theta$ is in Quadrant III, find $\cos\theta$.
If $\sin\theta = -\dfrac{3}{5}$ and $\theta$ is in Quadrant III, find $\cos\theta$.
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$\cos\theta = -\dfrac{4}{5}$ (In Quadrant III, both sine and cosine are negative; use $\sin^2\theta + \cos^2\theta = 1$)
$\cos\theta = -\dfrac{4}{5}$ (In Quadrant III, both sine and cosine are negative; use $\sin^2\theta + \cos^2\theta = 1$)
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What is $\sin 270°$?
What is $\sin 270°$?
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$-1$
$-1$
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What are the three reciprocal trig functions?
What are the three reciprocal trig functions?
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$\csc\theta = \dfrac{1}{\sin\theta}$, $\sec\theta = \dfrac{1}{\cos\theta}$, $\cot\theta = \dfrac{1}{\tan\theta}$
$\csc\theta = \dfrac{1}{\sin\theta}$, $\sec\theta = \dfrac{1}{\cos\theta}$, $\cot\theta = \dfrac{1}{\tan\theta}$
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In a triangle, $a = 5$, $b = 7$, and angle $C = 60°$. Find side $c$ using the law of cosines.
In a triangle, $a = 5$, $b = 7$, and angle $C = 60°$. Find side $c$ using the law of cosines.
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$c = \sqrt{39}$ (Use $c^2 = 25 + 49 - 2(5)(7)\cos 60° = 74 - 70(\tfrac{1}{2}) = 74 - 35 = 39$)
$c = \sqrt{39}$ (Use $c^2 = 25 + 49 - 2(5)(7)\cos 60° = 74 - 70(\tfrac{1}{2}) = 74 - 35 = 39$)
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What is $\tan 0°$?
What is $\tan 0°$?
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$0$
$0$
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Convert $60°$ to radians.
Convert $60°$ to radians.
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$\dfrac{\pi}{3}$ ($60 \times \dfrac{\pi}{180} = \dfrac{\pi}{3}$)
$\dfrac{\pi}{3}$ ($60 \times \dfrac{\pi}{180} = \dfrac{\pi}{3}$)
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What is the law of sines?
What is the law of sines?
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$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$ where $a, b, c$ are sides opposite angles $A, B, C$
$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$ where $a, b, c$ are sides opposite angles $A, B, C$
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In which quadrants is tangent positive?
In which quadrants is tangent positive?
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Quadrants I and III (where sine and cosine have the same sign). Mnemonic: ASTC - Tangent in III.
Quadrants I and III (where sine and cosine have the same sign). Mnemonic: ASTC - Tangent in III.
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What is the alternate form of $\tan\theta$ in terms of sine and cosine?
What is the alternate form of $\tan\theta$ in terms of sine and cosine?
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$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$
$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$
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