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Who remembers the Trig Who remembers the Trig Functions?Functions?
SineSine
TangentTangent
CosineCosine
Basic definitions In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.The shape of a right triangle is completely determined, up to similarity, by the value of either of the other two angles. This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the size of the triangle.
These ratios are traditionally described by the following trigonometric functions of the known angle:
(2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site: http://en.wikipedia.org/wiki/Trigonometry
The sine function (sin), defined as the ratio of the leg opposite the angle to the hypotenuse.
The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse. The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg. The adjacent leg is the side of the angle that is not the hypotenuse. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle. (2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site: http://en.wikipedia.org/wiki/Trigonometry
(2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site: http://en.wikipedia.org/wiki/Trigonometry
In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.
Trig Functions
When will we use trig?When will we use trig?
http://teachertube.com/http://teachertube.com/viewVideo.php?viewVideo.php?video_id=100065&title=video_id=100065&title=Using_Trig_in_Real_Life Using_Trig_in_Real_Life
Do you a have a creative Do you a have a creative way to remember the way to remember the
ratios?ratios?
The sine, cosine and tangent ratios in right triangles can be remembered by
SOH CAH TOA (sine-opposite-hypotenuse cosine-adjacent-hypotenuse tangent-
opposite-adjacent).
It is commonly referred to as "Sohcahtoa" by some American mathematics teachers, who liken it to a (nonexistent) Native American
girl's or mountain's name.
(2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site: http://en.wikipedia.org/wiki/Trigonometry
What about a 45What about a 45°-45-45°-90-90° ΔΔ
B
A
C
21
1
Sin<A =
Cos<A =
Tan<A =
You can find the sin, cos and tan of either angle.
Find them for <B.
The angle can be named <A or sin 45°
What about a 30What about a 30°-60-60°-90-90° ΔΔ ??
A
B
C
12
3
Sin<A =
Cos<A =
Tan<A =
Try this one!Try this one!
C
B
A
63
3 3
Look for a pattern:Look for a pattern:
If you find out that the sine of If you find out that the sine of an angle is equal to .5 or ½, an angle is equal to .5 or ½, what can you say about the what can you say about the
angle? What can you say angle? What can you say about the triangle if it has a about the triangle if it has a
right angle?right angle?
If the sine of one angle is ½ and the triangle is a right triangle, you have a 30-60-90 triangle.
Learn these!!!!Learn these!!!!