Download 6.2 - Math TAMU

1
c
Marcia
Drost, March 7, 2008
150 Lecture Notes - Section 6.2
Trigonometry of Right Triangles
sin θ =
opposite
hypotenuse
csc θ =
hypotenuse
opposite
cos θ =
adjacent
hypotenuse
sec θ =
hypotenuse
adjacent
tan θ =
opposite
adjacent
cot θ =
adjacent
opposite
Find the values of the six trigonometric
functions of θ
4
32 + 42 = (hyp)2
25 = (hyp)2
θ
5 = hyp
3
sin θ =
4
5
csc θ =
5
4
cos θ =
3
5
sec θ =
5
3
tan θ =
4
3
cot θ =
3
4
√
2
1
sin 45 = √ =
2
2
√
1
2
o
cos 45 = √ =
2
2
o
tan 45 = 1
o
csc 45o =
√
sec 45 =
√
o
2
2
1
45
1
cot 45 = 1
o
ο
2
c
Marcia
Drost, March 7, 2008
sin 30o =
cos 30o =
1
2
√
3
2
cot 30o =
√
tan 60o =
3
2
3
sec 60o = 2
60
√
3
1
cot 60o = √ =
3
3
3
1
Cofunctions of Complementary angles are Equal
sin (90o − θ) = cos θ
cos (90o − θ) = sin θ
tan (90o − θ) = cot θ
sec (90o − θ) = csc θ
Fundamental Trigonometric Identities
reciprocal identities
sin θ =
1
csc θ
cos θ =
1
sec θ
tan θ =
1
cot θ
csc θ =
1
sin θ
sec θ =
1
cos θ
cot θ =
1
tan θ
quotient identities
tan θ =
3
o
1
2
√
√
√
2
2 3
csc 60 = √ =
3
3
3
sin 60 =
2
cos 60o =
30
2
2 3
sec 30o = √ =
3
3
1
3
tan 30o = √ =
3
3
sin θ
cos θ
1
ο
√
√
o
2
csc 30o = 2
cot θ =
cos θ
sin θ
ο
c
Marcia
Drost, March 7, 2008
3
To solve a Triangle: means to find the size of the three angles, and the length of the
three sides.
Finding the height of a plane.: A plane is spotted 2 miles away at an angle of elevation
of 25o . Find the altitude of the plane.
From a point on the ground 500 ft. from the base of a building, and observer finds the
angle of elevation to the top of the building is 24o and the angle of elevation to the top
of a flagpole atop the building is 27o . Find the height of the building and the height
of the flagpole.