Download Right Triangle Trig Ratios

 #1 Notes
13.1
Right Triangle Trigonometry
#1 Algebra 2 Notes
13.1 Right Triangle Trigonometry
Algebra:
the study of mathematics in which letters and
other symbols are used to represent number
and quantities in formulas and equations
Geometry:
the study of mathematics that deals with
points, lines, angles, surfaces, and solids
Trigonometry:
the study of mathematics that deals with
the relations between the sides and angles
of triangles [right and non­right triangles]
Consider a Right Triangle, one of whose acute angles
[less than 90 o ] is 0 . 0 is a Greek letter and
pronouned "Theta"
other Greek letters:
Alpha
Beta
Gamma
Theta
The three sides of a triangle are the
Hypotenuse, the side opposite 0 , and the side
next to 0 called the adjacent side
[Abbreviated as HYP, OPP, ADJ]
Name the sides of each triangle:
1)
2)
OPP ADJ HYP
3)
Ratios [Fractions] of a right triangle's 3 sides are
used to define the six Trigonometric Functions:
Trigonometric Functions and their abbreviations:
Sine
Cosecant
Cosine
Secant
Tangent
Cotangent
Let 0 be an acute angle of a right triangle. The 6 [Trig]
Trigonometric functions of 0 are defined as follows:
Sin =
Csc
=
Cos =
Sec
=
Tan
Cot
=
=
Note:These last 3 functions are reciprocals of the first 3
This is where SOH­CAH­TOA comes from
Remember:
Pythagorean
Theorem
a 2 + b2 = c 2 Note:
adj = adjacent
opp = opposite
hyp = hypotenuse Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
1.
3
4
2.
3
6
1
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
3.
52
5
4.
7
15
1
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember
5.
19
9
6.
15
9
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember
7.
24
16
8.
6
3 5
#1 Notes
13.1
Right Triangle Trigonometry
#1 Algebra 2 Notes
13.1 Right Triangle Trigonometry
Algebra:
the study of mathematics in which letters and
other symbols are used to represent number
and quantities in formulas and equations
Geometry:
the study of mathematics that deals with
points, lines, angles, surfaces, and solids
Trigonometry:
the study of mathematics that deals with
the relations between the sides and angles
of triangles [right and non­right triangles]
Consider a Right Triangle, one of whose acute angles
[less than 90 o ] is 0 . 0 is a Greek letter and
pronouned "Theta"
other Greek letters:
Alpha
Beta
Gamma
Theta
The three sides of a triangle are the
Hypotenuse, the side opposite 0 , and the side
next to 0 called the adjacent side
[Abbreviated as HYP, OPP, ADJ]
Name the sides of each triangle:
1)
2)
3)
Ratios [Fractions] of a right triangle's 3 sides are
used to define the six Trigonometric Functions:
Trigonometric Functions and their abbreviations:
Sine
Cosecant
Cosine
Secant
Tangent
Cotangent
Let 0 be an acute angle of a right triangle. The 6
Trigonometric [Trig] functions of 0 are defined as
follows:
Sin =
Csc
=
Cos =
Sec
=
Tan
Cot
=
=
Note:These last 3 functions are reciprocals of the first 3
This is where SOH­CAH­TOA comes from
Remember:
Pythagorean
Theorem
a 2 + b2 = c 2 Note:
adj = adjacent
opp = opposite
hyp = hypotenuse Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
1.
3
4
2.
3
6
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
3.
sin =
52
5
5
1
2
=
cos =
tan = 5 = 1
5
csc =
2
sec =
2
cot =
4.
1
7
15
15
7
15
7
15
15
= 15
=
4 11
44
15
7
7
= 47 11 = 7
44
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
5.
19
9
6.
15
9
1
Evaluate the 6 Trig functions of the angle 0 shown in
the right triangle: Remember to rationalize your answers
7.
24
16
162 + adj2 = 242
256 + adj2 = 576
­256
­256
adj2 = 320
adj = 320
adj = 8 5
8. 6
3 5
1