Solving Right Triangles: Pythagorean Theorem, Trigonometry - Geometry
Card 1 of 30
Find and correct the identity error: $\cos(\theta)=\cos(90^\circ-\theta)$.
Find and correct the identity error: $\cos(\theta)=\cos(90^\circ-\theta)$.
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Correct: $\cos(\theta)=\sin(90^\circ-\theta)$. Cosine equals sine of complement, not cosine of complement.
Correct: $\cos(\theta)=\sin(90^\circ-\theta)$. Cosine equals sine of complement, not cosine of complement.
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If $\cos(\theta)=\sin(18^\circ)$ and $\theta$ is acute, what is $\theta$?
If $\cos(\theta)=\sin(18^\circ)$ and $\theta$ is acute, what is $\theta$?
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$\theta=72^\circ$. Since $\cos(\theta) = \sin(18^\circ)$, then $\theta = 90^\circ - 18^\circ$.
$\theta=72^\circ$. Since $\cos(\theta) = \sin(18^\circ)$, then $\theta = 90^\circ - 18^\circ$.
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If $\sin(\theta)=\cos(\theta)$ and $\theta$ is acute, what is $\theta$?
If $\sin(\theta)=\cos(\theta)$ and $\theta$ is acute, what is $\theta$?
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$\theta=45^\circ$. Only at $45^\circ$ are sine and cosine equal.
$\theta=45^\circ$. Only at $45^\circ$ are sine and cosine equal.
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If $\sin(\alpha)=\cos(\beta)$ and both angles are acute, what must be true about $\alpha$ and $\beta$?
If $\sin(\alpha)=\cos(\beta)$ and both angles are acute, what must be true about $\alpha$ and $\beta$?
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$\alpha+\beta=90^\circ$. The cofunction identity requires complementary angles.
$\alpha+\beta=90^\circ$. The cofunction identity requires complementary angles.
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In a right triangle, if one acute angle is $\theta$, what is the other acute angle in degrees?
In a right triangle, if one acute angle is $\theta$, what is the other acute angle in degrees?
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$90^\circ-\theta$. Right triangles have two acute angles that sum to $90^\circ$.
$90^\circ-\theta$. Right triangles have two acute angles that sum to $90^\circ$.
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In a right triangle, if one acute angle is $\theta$, what is the other acute angle in radians?
In a right triangle, if one acute angle is $\theta$, what is the other acute angle in radians?
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$\frac{\pi}{2}-\theta$. Right triangles have two acute angles that sum to $\frac{\pi}{2}$.
$\frac{\pi}{2}-\theta$. Right triangles have two acute angles that sum to $\frac{\pi}{2}$.
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In a right triangle, which function of $\theta$ equals the ratio adjacent over hypotenuse?
In a right triangle, which function of $\theta$ equals the ratio adjacent over hypotenuse?
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$\cos(\theta)$. Cosine is defined as adjacent over hypotenuse.
$\cos(\theta)$. Cosine is defined as adjacent over hypotenuse.
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In a right triangle, which function of $\theta$ equals the ratio opposite over hypotenuse?
In a right triangle, which function of $\theta$ equals the ratio opposite over hypotenuse?
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$\sin(\theta)$. Sine is defined as opposite over hypotenuse.
$\sin(\theta)$. Sine is defined as opposite over hypotenuse.
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In a right triangle, if the acute angles are $\theta$ and $90^\circ-\theta$, what is $\sin(\theta)$ equal to?
In a right triangle, if the acute angles are $\theta$ and $90^\circ-\theta$, what is $\sin(\theta)$ equal to?
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$\cos(90^\circ-\theta)$. Using the cofunction identity in right triangles.
$\cos(90^\circ-\theta)$. Using the cofunction identity in right triangles.
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In a right triangle, if the acute angles are $\theta$ and $90^\circ-\theta$, what is $\cos(\theta)$ equal to?
In a right triangle, if the acute angles are $\theta$ and $90^\circ-\theta$, what is $\cos(\theta)$ equal to?
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$\sin(90^\circ-\theta)$. Using the cofunction identity in right triangles.
$\sin(90^\circ-\theta)$. Using the cofunction identity in right triangles.
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What is $\sin(0^\circ)$ rewritten as a cosine of a complementary angle?
What is $\sin(0^\circ)$ rewritten as a cosine of a complementary angle?
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$\sin(0^\circ)=\cos(90^\circ)$. Since $0^\circ + 90^\circ = 90^\circ$, they are complementary.
$\sin(0^\circ)=\cos(90^\circ)$. Since $0^\circ + 90^\circ = 90^\circ$, they are complementary.
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What is $\cos(0^\circ)$ rewritten as a sine of a complementary angle?
What is $\cos(0^\circ)$ rewritten as a sine of a complementary angle?
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$\cos(0^\circ)=\sin(90^\circ)$. Since $0^\circ + 90^\circ = 90^\circ$, they are complementary.
$\cos(0^\circ)=\sin(90^\circ)$. Since $0^\circ + 90^\circ = 90^\circ$, they are complementary.
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Find and correct the identity error: $\cos(\theta)=\cos(90^\circ-\theta)$.
Find and correct the identity error: $\cos(\theta)=\cos(90^\circ-\theta)$.
Tap to reveal answer
Correct: $\cos(\theta)=\sin(90^\circ-\theta)$. Cosine equals sine of complement, not cosine of complement.
Correct: $\cos(\theta)=\sin(90^\circ-\theta)$. Cosine equals sine of complement, not cosine of complement.
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What is $\sin(90^\circ)$ rewritten as a cosine of a complementary angle?
What is $\sin(90^\circ)$ rewritten as a cosine of a complementary angle?
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$\sin(90^\circ)=\cos(0^\circ)$. Since $90^\circ + 0^\circ = 90^\circ$, they are complementary.
$\sin(90^\circ)=\cos(0^\circ)$. Since $90^\circ + 0^\circ = 90^\circ$, they are complementary.
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What is $\cos(90^\circ)$ rewritten as a sine of a complementary angle?
What is $\cos(90^\circ)$ rewritten as a sine of a complementary angle?
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$\cos(90^\circ)=\sin(0^\circ)$. Since $90^\circ + 0^\circ = 90^\circ$, they are complementary.
$\cos(90^\circ)=\sin(0^\circ)$. Since $90^\circ + 0^\circ = 90^\circ$, they are complementary.
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Find the complement: If $\theta=23^\circ$, what is $90^\circ-\theta$?
Find the complement: If $\theta=23^\circ$, what is $90^\circ-\theta$?
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$67^\circ$. Complementary angles sum to $90^\circ$.
$67^\circ$. Complementary angles sum to $90^\circ$.
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Find the complement: If $\theta=58^\circ$, what is $90^\circ-\theta$?
Find the complement: If $\theta=58^\circ$, what is $90^\circ-\theta$?
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$32^\circ$. Complementary angles sum to $90^\circ$.
$32^\circ$. Complementary angles sum to $90^\circ$.
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Find the complement: If $\theta=11^\circ$, what is $90^\circ-\theta$?
Find the complement: If $\theta=11^\circ$, what is $90^\circ-\theta$?
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$79^\circ$. Complementary angles sum to $90^\circ$.
$79^\circ$. Complementary angles sum to $90^\circ$.
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Find the complement: If $\theta=\frac{\pi}{8}$, what is $\frac{\pi}{2}-\theta$?
Find the complement: If $\theta=\frac{\pi}{8}$, what is $\frac{\pi}{2}-\theta$?
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$\frac{3\pi}{8}$. Complementary angles sum to $\frac{\pi}{2}$.
$\frac{3\pi}{8}$. Complementary angles sum to $\frac{\pi}{2}$.
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Find the complement: If $\theta=\frac{\pi}{3}$, what is $\frac{\pi}{2}-\theta$?
Find the complement: If $\theta=\frac{\pi}{3}$, what is $\frac{\pi}{2}-\theta$?
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$\frac{\pi}{6}$. Complementary angles sum to $\frac{\pi}{2}$.
$\frac{\pi}{6}$. Complementary angles sum to $\frac{\pi}{2}$.
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Find and correct the identity error: $\sin(\theta)=\sin(90^\circ-\theta)$.
Find and correct the identity error: $\sin(\theta)=\sin(90^\circ-\theta)$.
Tap to reveal answer
Correct: $\sin(\theta)=\cos(90^\circ-\theta)$. Sine equals cosine of complement, not sine of complement.
Correct: $\sin(\theta)=\cos(90^\circ-\theta)$. Sine equals cosine of complement, not sine of complement.
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What is the complementary-angle identity that relates $\sin(\theta)$ to a cosine expression?
What is the complementary-angle identity that relates $\sin(\theta)$ to a cosine expression?
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$\sin(\theta)=\cos(90^\circ-\theta)$. Sine of an angle equals cosine of its complement.
$\sin(\theta)=\cos(90^\circ-\theta)$. Sine of an angle equals cosine of its complement.
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What is the complementary-angle identity that relates $\cos(\theta)$ to a sine expression?
What is the complementary-angle identity that relates $\cos(\theta)$ to a sine expression?
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$\cos(\theta)=\sin(90^\circ-\theta)$. Cosine of an angle equals sine of its complement.
$\cos(\theta)=\sin(90^\circ-\theta)$. Cosine of an angle equals sine of its complement.
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What is $\sin(90^\circ-\theta)$ equal to in terms of $\cos(\theta)$?
What is $\sin(90^\circ-\theta)$ equal to in terms of $\cos(\theta)$?
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$\sin(90^\circ-\theta)=\cos(\theta)$. Sine of $90^\circ-\theta$ is the cosine of $\theta$.
$\sin(90^\circ-\theta)=\cos(\theta)$. Sine of $90^\circ-\theta$ is the cosine of $\theta$.
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What is $\cos(90^\circ-\theta)$ equal to in terms of $\sin(\theta)$?
What is $\cos(90^\circ-\theta)$ equal to in terms of $\sin(\theta)$?
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$\cos(90^\circ-\theta)=\sin(\theta)$. Cosine of $90^\circ-\theta$ is the sine of $\theta$.
$\cos(90^\circ-\theta)=\sin(\theta)$. Cosine of $90^\circ-\theta$ is the sine of $\theta$.
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What is the identity for $\sin(\theta)$ using radians and complementary angles?
What is the identity for $\sin(\theta)$ using radians and complementary angles?
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$\sin(\theta)=\cos\left(\frac{\pi}{2}-\theta\right)$. Radian form: sine equals cosine of complement.
$\sin(\theta)=\cos\left(\frac{\pi}{2}-\theta\right)$. Radian form: sine equals cosine of complement.
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What is the identity for $\cos(\theta)$ using radians and complementary angles?
What is the identity for $\cos(\theta)$ using radians and complementary angles?
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$\cos(\theta)=\sin\left(\frac{\pi}{2}-\theta\right)$. Radian form: cosine equals sine of complement.
$\cos(\theta)=\sin\left(\frac{\pi}{2}-\theta\right)$. Radian form: cosine equals sine of complement.
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What is $\sin\left(\frac{\pi}{2}-\theta\right)$ equal to in terms of $\cos(\theta)$?
What is $\sin\left(\frac{\pi}{2}-\theta\right)$ equal to in terms of $\cos(\theta)$?
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$\sin\left(\frac{\pi}{2}-\theta\right)=\cos(\theta)$. Sine of complement equals cosine of original angle.
$\sin\left(\frac{\pi}{2}-\theta\right)=\cos(\theta)$. Sine of complement equals cosine of original angle.
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What is $\cos\left(\frac{\pi}{2}-\theta\right)$ equal to in terms of $\sin(\theta)$?
What is $\cos\left(\frac{\pi}{2}-\theta\right)$ equal to in terms of $\sin(\theta)$?
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$\cos\left(\frac{\pi}{2}-\theta\right)=\sin(\theta)$. Cosine of complement equals sine of original angle.
$\cos\left(\frac{\pi}{2}-\theta\right)=\sin(\theta)$. Cosine of complement equals sine of original angle.
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What does it mean for angles $\alpha$ and $\beta$ to be complementary in degrees?
What does it mean for angles $\alpha$ and $\beta$ to be complementary in degrees?
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$\alpha+\beta=90^\circ$. Two angles are complementary when they sum to $90^\circ$.
$\alpha+\beta=90^\circ$. Two angles are complementary when they sum to $90^\circ$.
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