13.4 and 13.5 basic trig. today we will… find the sine, cosine, and tangent values for angles. we...
TRANSCRIPT
13.4 and 13.5Basic 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.
New Words
Trigonometry:the study of the properties of
triangles.Trigonometric ratio:
ratio of the measures of 2 sides of a triangle.
New Words
Sine: written sin, read [sahyn]Cosine: written cos, read [koh-sahyn]Tangent: written tan, read [tan- juhnt)
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)
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
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.
Right Triangle
HypotenuseAdjacent Opposite
If we are talking about this angle then...
Right Triangle
HypotenuseAdjacent Opposite
If we are talking about this angle then...
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
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
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
What’s up with the sayingsSome old horse, caught another horse, taking oats away.
sin =opphyp cos =
adjhyp tan =
oppadj
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
New Words
Angle of depression
Angle of elevation
Find tan j
k
3
6tan J =
oppadj
36
jl
45
Find cos j
k
3
6cos J =
adjhyp
645
jl
45 now simplify
Find tan k
k
5
12tan K =
oppadj
12 5
jl
13
Find sin k
k
5
12sin K =
opphyp
1213
jl
13
Find cos k
k
5
12cos K =
adjhyp
513
jl
13
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
To find a side...What ratio can we use?
210cos 18 =
adjhyp
?210
?18 What sides do we know?
.9511 X 210 = ?
.9511 = ?210
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
To find an angle...What ratio can we use?
3078sin ? =
opphyp
6003078
?
600
What sides do we know?
= .1949
sin-1 .1949 = 11.24
Make sure your calculator is in degrees not radians
When calculating trig functions, we usually round to 4 decimal places