SAT Math Flashcards - SAT Math
Card 0 of 25
Convert one degree to radians.
Convert one degree to radians.
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In order to change degrees to radians we need to multiply the degrees by 
:
In order to change degrees to radians we need to multiply the degrees by
Convert one radian to degrees.
Convert one radian to degrees.
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In order to change radians to degrees we need to multiply radians by 
:
In order to change radians to degrees we need to multiply radians by
Define tangent in a right triangle.
Define tangent in a right triangle.
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$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$.
$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$.
Find $\sin \theta$ if opposite = 5, hypotenuse = 13.
Find $\sin \theta$ if opposite = 5, hypotenuse = 13.
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$\sin \theta = 5/13$.
$\sin \theta = 5/13$.
Find hypotenuse if $\cos \theta = 0.8$ and adjacent = 12.
Find hypotenuse if $\cos \theta = 0.8$ and adjacent = 12.
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$h = 12 / 0.8 = 15$.
$h = 12 / 0.8 = 15$.
Find missing side if $\sin \theta = 0.6$ and hypotenuse = 10.
Find missing side if $\sin \theta = 0.6$ and hypotenuse = 10.
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Opposite $= 6$.
Opposite $= 6$.
Find the hypotenuse if legs are 6 and 8.
Find the hypotenuse if legs are 6 and 8.
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$\sqrt{6^2 + 8^2} = 10$.
$\sqrt{6^2 + 8^2} = 10$.
In a $30^{\circ}$–$60^{\circ}$–$90^{\circ}$ triangle, if the short leg = 5, find hypotenuse.
In a $30^{\circ}$–$60^{\circ}$–$90^{\circ}$ triangle, if the short leg = 5, find hypotenuse.
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$10$.
$10$.
In a $45^{\circ}$–$45^{\circ}$–$90^{\circ}$ triangle, if a leg = 4, find hypotenuse.
In a $45^{\circ}$–$45^{\circ}$–$90^{\circ}$ triangle, if a leg = 4, find hypotenuse.
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$4\sqrt{2}$.
$4\sqrt{2}$.
List the common Pythagorean triples.
List the common Pythagorean triples.
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$(3,4,5)$, $(5,12,13)$, $(7,24,25)$, $(8,15,17)$.
$(3,4,5)$, $(5,12,13)$, $(7,24,25)$, $(8,15,17)$.
What are the sides in a right triangle called?
What are the sides in a right triangle called?
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Legs and hypotenuse.
Legs and hypotenuse.
What is the hypotenuse?
What is the hypotenuse?
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The side opposite the right angle, and the longest side in a right triangle.
The side opposite the right angle, and the longest side in a right triangle.
Define cosine in a right triangle.
Define cosine in a right triangle.
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$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.
Define a tangent.
Define a tangent.
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A line that touches the circle at exactly one point.
A line that touches the circle at exactly one point.
Define cotangent, secant, and cosecant.
Define cotangent, secant, and cosecant.
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$\cot \theta = \frac{1}{\tan \theta}$, $\sec \theta = \frac{1}{\cos \theta}$, $\csc \theta = \frac{1}{\sin \theta}$.
$\cot \theta = \frac{1}{\tan \theta}$, $\sec \theta = \frac{1}{\cos \theta}$, $\csc \theta = \frac{1}{\sin \theta}$.
How does the sine of an acute angle compare to the cosine of its complement?
How does the sine of an acute angle compare to the cosine of its complement?
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They are equal: $\sin \theta = \cos(90^{\circ} - \theta)$.
They are equal: $\sin \theta = \cos(90^{\circ} - \theta)$.
Law of Cosines formula.
Law of Cosines formula.
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$c^2 = a^2 + b^2 - 2ab\cos C$.
$c^2 = a^2 + b^2 - 2ab\cos C$.
Law of Sines formula.
Law of Sines formula.
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$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.
Quotient identity for tangent.
Quotient identity for tangent.
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$\tan \theta = \frac{\sin \theta}{\cos \theta}$.
$\tan \theta = \frac{\sin \theta}{\cos \theta}$.
What is the formula for the area of a triangle using sine?
What is the formula for the area of a triangle using sine?
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$A = \tfrac{1}{2}ab\sin C$.
$A = \tfrac{1}{2}ab\sin C$.
What is the trig identity connecting sine and cosine?
What is the trig identity connecting sine and cosine?
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$\sin^2 \theta + \cos^2 \theta = 1$.
$\sin^2 \theta + \cos^2 \theta = 1$.
When is the Law of Cosines used?
When is the Law of Cosines used?
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For triangles where two sides and included angle (SAS) or all three sides (SSS) are known.
For triangles where two sides and included angle (SAS) or all three sides (SSS) are known.
When is the Law of Sines used?
When is the Law of Sines used?
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For non-right triangles with known angle–side pairs (AAS, ASA, SSA).
For non-right triangles with known angle–side pairs (AAS, ASA, SSA).
What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
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$a^2 + b^2 = c^2$ (for right triangles).
$a^2 + b^2 = c^2$ (for right triangles).
Define sine in a right triangle.
Define sine in a right triangle.
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$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$.