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