Download trigonometric ratio

Lesson 12.1A ADV:
1. Homework Discussion
2. Trigonometric Ratios
Warm Up:
• Solve for x.
a) 12 =
c)
𝑥
5
.8 =
𝑥
12
b) 30 =
6
𝑥
d) 0.453 =
5
𝑥
Intro to Trigonometry:
• Trigonometry is the study of the relationships
between the sides and the angles of triangles.
We will be focusing on right triangles for now.
Sides of a Triangle:
• Opposite an Angle.
• Adjacent to an Angle.
• Hypotenuse.
Ratio of Sides:
• What is the ratio of the side across from (opposite) the given angle to the
side next to (adjacent) the given angle. Find the ratio for each triangle.
• What conclusions can you draw about a 31° angle?
Trig Ratios – Example A:
Finding Trigonometric Ratios
A trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
The word trigonometry is derived from the ancient Greek language and means measurement
of triangles.
The three basic trigonometric ratios are sine, cosine, and tangent, which are
abbreviated as sin, cos, and tan, respectively.
Finding Trigonometric Ratios
A trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
TRIGONOMETRIC RATIOS
Let
ABC be a right triangle. The sine, the cosine, and the tangent of the acute
angle A are defined as follows.
sin A =
side opposite A
hypotenuse
cos A =
side adjacent A
hypotenuse
tan A =
side opposite A
side adjacent to A
B
=
hypotenuse
c
=
A
=
side
a opposite
A
C
b
side adjacent to A
The value of the trigonometric ratio depends only on the measure of the acute
angle, not on the particular right triangle that is used to compute the value.
Example Continued:
• So, let’s revisit the slide with the 31° angles. From the 31°
angle, which sides are we dealing with?
• Which trigonometric ratio are we dealing with?
• Therefore, the ____________ of all 31° angles is 0.6.
HW Summary/Discussion:
• Take out your post-test homework again.
Identify which ratio is sin, cos, and then tan
for ∠𝐴 in ∆𝐴𝐵𝐶.
• What is the measure of ∠𝐵?
• Now, find the sin, cos, and tan for angle B.
Calculator Use:
• Now, using the graphing calculator, determine
the following (round to 3 decimal places):
sin 37° =
cos 37° =
tan 37° =
sin 53° =
cos 53° =
tan 53° =
Example #1:
• Using trig ratios, determine the value of x.
A
70°
8
x
Example #2:
• Using trig ratios, determine the value of x.
Example #3:
• Using trig ratios, determine the value of x.
A
70°
x
65
Homework:
• P. 644-645: 3-5, 7, 14-16, 18, 21, 22