Objectives

1
Objectives

• Define and apply sine, cosine, and tangent in
  right triangles

2
Trigonometric Ratios for Right Triangles
By the AA Similarity Postulate, a right triangle
with a given acute angle is similar to every
other right triangle with that same acute angle
measure. So ?ABC ?DEF ?XYZ, and
. These are trigonometric ratios. A
trigonometric ratio is a ratio of two sides of a
right triangle.
3
Sine, Cosine, Tangent Definitions
SohCahToa
4
Story of Chief Soh Cah Toa

• A young Indian, frustrated by his inability to
  understand the geometric constructions of his
  tribe's battle dress, kicked out in anger against
  a stone and crushed his big toe. Fortunately, he
  learned from this experience, and began to use
  study and concentration to solve his problems
  rather than violence and injure himself. This was
  especially effective in his study of math, and he
  went on to become the wisest man of his tribe. He
  studied many aspects of trigonometry and even
  today we remember many of the functions by his
  name. When he became an adult, the tribal priest
  gave him a name that reflected his special nature
  -- one that reminded them of his great
  discoveries and of the event which changed his
  life. Because he was troubled throughout his life
  by the problematic toe that he injured by kicking
  the stone, he was constantly at the edge of the
  river, soaking his toe in the cooling waters. For
  that behavior, he was named Chief Soh Cah Toa.

5
Ex. 1

• Sin A ?
• Mark angle A.
• Label the sides in relation to angle A (opp, adj,
  hyp)
• Circle the sides that we use for sin
• Decide which side goes on top of the fraction
• Write the fraction

B
13
hyp
5
opp
A
C
12
adj
SohCahToa
Sin A 5/13
6
Ex. 2

• Cos B ?
• Mark angle B.
• Label the sides in relation to angle B (opp, adj,
  hyp)
• Circle the sides that we use for cos
• Decide which side goes on top of the fraction
• Write the fraction

B
13
hyp
5
adj
A
C
12
opp
SohCahToa
Cos B 5/13
7
Trigonometry with a Calculator Ex. 1

• x ?
• Mark angle A.
• Label the sides in relation to angle A (opp, adj,
  hyp)
• Decide which trig. func. You can use.
• Decide which side goes on top of the fraction
• Write the fraction
• Solve for x.

B
13
hyp
x
opp
34
A
C
adj
SohCahToa
Sin 34 x/13 x 13 sin 34 x 7.3
8
Trigonometry with a Calculator Ex. 4

• x ?
• Mark angle A.
• Label the sides in relation to angle A (opp, adj,
  hyp)
• Decide which trig. func. You can use.
• Decide which side goes on top of the fraction
• Write the fraction
• Solve for x.

B
x
hyp
20
opp
52
A
C
adj
SohCahToa
Sin 52 20/x x 20/sin 52 x 25.4
9
Inverse Trigonometric Functions
If you know the sine, cosine, or tangent of an
acute angle measure, you can use the inverse
trigonometric functions to find the measure of
the angle.
10
Finding an angle using Trig. Ex. 1

• x ?
• Mark angle A.
• Label the sides in relation to angle A (opp, adj,
  hyp)
• Decide which trig. func. You can use.
• Decide which side goes on top of the fraction
• Write the fraction
• Solve for x.

B
14
hyp
5
opp
x
A
C
adj
SohCahToa
Sin x 5/14 x sin-1(5/14) x 21
11
Finding an angle using Trig. Ex. 2

• x ?
• Mark angle A.
• Label the sides in relation to angle A (opp, adj,
  hyp)
• Decide which trig. func. You can use.
• Decide which side goes on top of the fraction
• Write the fraction
• Solve for x.

B
hyp
5
opp
x
A
C
14
adj
SohCahToa
Tan x 5/14 x tan-1(5/14) x 20