13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We...
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Transcript of 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We...
![Page 1: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/1.jpg)
13.4 and 13.5Basic Trig
![Page 2: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/2.jpg)
Today we will…
Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.
![Page 3: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/3.jpg)
New Words
Trigonometry:the study of the properties of
triangles.Trigonometric ratio:
ratio of the measures of 2 sides of a triangle.
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New Words
Sine: written sin, read [sahyn]Cosine: written cos, read [koh-sahyn]Tangent: written tan, read [tan- juhnt)
![Page 5: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/5.jpg)
New sayingsSome old horse, caught another horse, taking oats away.Signs of happiness come after having tankards of ale.Some of her children are having trouble over algebra.Some out houses can actually have totally odorless aromas.SOH CAH TOA (read soh-kuh-toh-uh)
![Page 6: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/6.jpg)
Right TriangleHas 3 sides:HypotenuseAdjacent Opposite
The Hypotenuse is always across from the right angle. It is the longest.
The other two will depend on what angle we are dealing with
![Page 7: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/7.jpg)
Right TriangleThe opposite side is across the triangle from the angle.
The adjacent side is next to the angle. It is one of the sides of the angle.
![Page 8: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/8.jpg)
Right Triangle
HypotenuseAdjacent Opposite
If we are talking about this angle then...
![Page 9: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/9.jpg)
Right Triangle
HypotenuseAdjacent Opposite
If we are talking about this angle then...
![Page 10: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/10.jpg)
Sine
Sine is the ratio of the opposite side divided by the hypotenuse.
B
5
4
3
sin B =opphyp
35
C
sin C =opphyp
45
![Page 11: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/11.jpg)
Cosine
Cosine is the ratio of the adjacent side divided by the hypotenuse.
B
5
4
3
cos B =adjhyp
45
C
cos C =adjhyp
35
![Page 12: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/12.jpg)
Tangent
tangent is the ratio of the opposite side divided by the adjacent.
B
5
4
3
tan B =oppadj
34
C
tan C =oppadj
43
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What’s up with the sayingsSome old horse, caught another horse, taking oats away.
sin =opphyp cos =
adjhyp tan =
oppadj
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Which ever one you like...Some old horse, caught another horse, taking oats away.Signs of happiness come after having tankards of ale.Some of her children are having trouble over algebra.Some out houses can actually have totally odorless aromas.SOH CAH TOA (read soh-kuh-toh-uh)
soak-a-toe-a
![Page 15: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/15.jpg)
New Words
Angle of depression
Angle of elevation
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Find tan j
k
3
6tan J =
oppadj
36
jl
45
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Find cos j
k
3
6cos J =
adjhyp
645
jl
45 now simplify
![Page 18: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/18.jpg)
Find tan k
k
5
12tan K =
oppadj
12 5
jl
13
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Find sin k
k
5
12sin K =
opphyp
1213
jl
13
![Page 20: 13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.](https://reader037.fdocuments.us/reader037/viewer/2022110103/5697bfa71a28abf838c9900c/html5/thumbnails/20.jpg)
Find cos k
k
5
12cos K =
adjhyp
513
jl
13
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To find a side...What ratio can we use?
13 tan 30 =oppadj
?13
?
30 What sides do we know?
.5774 X 13 = ?
.5774 = ?13
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To find a side...What ratio can we use?
210cos 18 =
adjhyp
?210
?18 What sides do we know?
.9511 X 210 = ?
.9511 = ?210
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To find an angle...What ratio can we use?
95
tan ? =oppadj
9540
?40
What sides do we know?
= 2.375
tan-1 2.375 = 67.17
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To find an angle...What ratio can we use?
3078sin ? =
opphyp
6003078
?
600
What sides do we know?
= .1949
sin-1 .1949 = 11.24
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Make sure your calculator is in degrees not radians
When calculating trig functions, we usually round to 4 decimal places