Introduction to trigonometric ratios

1
Introduction to trigonometric ratios

• Trigonometry is the study of the relationship
  between sides and angles of triangles.
• There are 3 basic ratios in trigonometry that can
  be used to find measures in right triangles

2
The 3 ratios are the sine of an angle, the cosine
of an angle, and the tangent of an angle

• A trigonometric ratio is a ratio of 2 sides of a
  right triangle

3
Trigonometric ratios

• In a right triangle, the sine of an angle is the
  ratio of the length of the leg opposite the angle
  to the length of the hypotenuse
• Sin A Opposite
• Hypotenuse

4
Trigonometric ratios

• In a right triangle, the cosine of a triangle is
  the ratio of the leg adjacent to the angle to the
  length of the hypotenuse
• Cos A Adjacent
• Hypotenuse

5
Trigonometric ratios

• In a right triangle, the tangent of an angle is
  the ratio of the leg opposite the angle to the
  length of the leg adjacent to the angle
• Tan A opposite
• adjacent

6
When used in equations, the sine, cosine, and
tangent are often abbreviated "sin", "cos", and
"tan"
7
Mnemonics can help you remember the trig ratios

• SOHCAHTOA
• or
• Studying Our Homework Can Always Help To Obtain
  Achievement

8
Find the sin, cos, and tan of angle S

• Sin a cos b tan a
• c c b

S
b
c
U
T
a
9
Find sin, cos, and tan of angle G
3
4
10
Use a calculator to evaluate the sine, cosine and
tangent of an angle

• Your calculator needs to be in DEGREE mode, not
  in radian mode

11
Use a calculator to evaluate each expression

• Round to nearest hundredth
• A) cos 72o
• B) sin 30o
• C) tan 70o
• D) cos 30o
• E) tan 45o
• F) sin 25o

12

• Trig ratios can be used to solve for unknown side
  lengths in right triangles.
• An equation can be divided or multiplied by a
  trig ratio, just as it can with any real number

13
Solving for side lengths

• Use Tangent ratio to find e to the nearest
  hundredth

13
72
e
14
Solving for side lengths

• Use sin to find x to the nearest hundredth

x
8
32
15
T
5
U
12
V

• Find sin ltT
• Find tan ltU
• Find cos ltT
• Find sin ltU
• Find cos ltU
• Find tan ltT

16
Z
W
39
x
41
Y

• Find x to the nearest tenth

17
Evaluate each expression

• Sin 30o
• Cos 90o
• Tan 45o