Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.
-
Upload
preston-thornton -
Category
Documents
-
view
235 -
download
0
Transcript of Right Triangle Trigonometry SO H CA H TO A CH O SH A CA O.
Right Triangle Trigonometry
SOH CAH TOA
CHO SHA CAO
Warm-up
Find the 6 trig function of
θ = 13800
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
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
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° = =
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
Finding Values of Irregular angles
sin 300 = .50
cos 1800 = .-1
sin 230 = .39073
tan 150 = .26795
sin 950 = .99619
cos 1090 = -.3257
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
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
= x√312
Solve x:
1260
xopp
adj
Tan 600
opp
adj
= =x
12
tan 600 =x
12√3
=x√3(12)