Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

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Right Triangle Trigonometry SOH CAH TOA CHO SHA CAO

Transcript of Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Page 1: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Right Triangle Trigonometry

SOH CAH TOA

CHO SHA CAO

Page 2: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Warm-up

Find the 6 trig function of

θ = 13800

Page 3: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

θ

The sides of the right triangle are:

· and the hypotenuse

opp· the side adjacent

adj

· the side opposite hyp

The trigonometric functions are

SOH CAH TOA

CHO SHA CAO

Page 4: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Example:Calculate the trigonometric functions for ∠θ .

The six trig ratios are

4

3

5

θ

sin θ =

tan θ =

sec θ =cos θ =

cot θ =

csc θ =

opp

adj

hyp

Page 5: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Your Turn!Calculate the trigonometric functions for a 30° angle.

12

30

csc 30° = = = 2 opp

hyp

sec 30° = = = adj

hypcos 30° = = hyp

adj

tan 30° = = = adj

oppcot 30° = = = opp

adj

sin 30° = =

Page 6: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Fundamental Trigonometric Identities

Cofunction Identities

sin θ = cos(90°− θ ) cos θ = sin(90°− θ )tan θ = cot(90°− θ ) cot θ = tan(90°− θ )sec θ = csc(90°− θ ) csc θ = sec(90°− θ )

Reciprocal Identities

sin θ = 1/csc θ cos θ = 1/sec θ tan θ = 1/cot θcot θ = 1/tan θ sec θ = 1/cos θ csc θ = 1/sin θ

Quotient Identities

tan θ = sin θ /cos θ cot θ = cos θ /sin θ

Pythagorean Identities

sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ cot2 θ + 1 = csc2 θ

Page 7: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Finding Values of Irregular angles

sin 300 = .50

cos 1800 = .-1

sin 230 = .39073

tan 150 = .26795

sin 950 = .99619

cos 1090 = -.3257

Page 8: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Solve x:7

30

xopp

hyp

Sin 300

opp

hyp

= =7

x

Sin 300 =7

x

1

2

=71 x (2)

x = 14

307

14

Page 9: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

Your TurnSolve x:

7

45

x

adj

hyp

cos 45

adj

hyp

= =7

x

cos 450 =7

x

√2

2

=7x (2)

307

7 √2

√2

=14x√2

√2 √2

= 7x √2

Page 10: Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.

= x√312

Solve x:

1260

xopp

adj

Tan 600

opp

adj

= =x

12

tan 600 =x

12√3

=x√3(12)