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5-MINUTE CHECKS
7.6 APPLY THE SINE AND COSINE RATIOS



Students will recognize and apply the sine & cosine
ratios where applicable.
Why? So you can find distances, as seen in EX 39.
Mastery is 80% or better on 5-minute checks and
practice problems.
TRIGONOMETRIC RATIOS- CONCEPT DEVELOP

Let ∆ABC be a right
triangle. The since,
the cosine, and the hypotenusec
tangent of the acute
angle A are
b
defined as follows. A side adjacent
to angle A
cos A =
sin A =
Side opposite A
hypotenuse
=
B
Side
a opposite
angle A
C
Side adjacent to A b
=
hypotenuse
c
a
c
tan A =
Side opposite A
a
=
Side adjacent to A b
EXAMPLE 1 – SKILL DEVELOP
THINK ….INK….SHARE
EXAMPLE 2 FINDING THE COSINE – SKILL
DEVELOP
EXAMPLE 3 -HOTS
THINK….INK….SHARE
EXAMPLE 3 SOLUTIONS
WITH A PARTNER
EXAMPLE 4 – HOTS FINDING A HYPOTENUSE
USING AN ANGLE OF DEPRESSION
EXAMPLE 4 SOLUTION
CHECK FOR UNDERSTANDING
EXAMPLE 5 FIND LEG LENGTH USING ANGLES
OF ELEVATION- REAL WORLD APPLICATION
EXAMPLE 5 SOLUTION
EXAMPLE 5 SOLUTION
EXAMPLE 6 USING SPECIAL RIGHT TRIANGLES –
GUIDED PRACTICE & APK
EXAMPLE 6 CONTINUED
THINK …..INK….SHARE
When looking for missing lengths & angle
measures what is the determining factor in
deciding to use Sin, Cos & Tan?
 How do you know which on to use?

WHAT WAS THE OBJECTIVE FOR TODAY?
Students will recognize and apply the sine &
cosine ratios where applicable.
 Why? So you can find distances, as seen in EX
39.
 Mastery is 80% or better on 5-minute checks
and practice problems.

HOMEWORK
Sin-Cos-Tan Practice PDF
 Teachers Web

EX: 5 USING A CALCULATOR

You can use a calculator to approximate the
sine, cosine, and the tangent of 74. Make
sure that your calculator is in degree mode.
The table shows some sample keystroke
sequences accepted by most calculators.
SAMPLE KEYSTROKES
Sample keystroke
sequences
74 sin
sin 74
Sample calculator display
Rounded
Approximation
0.961262695
0.9613
0.275637355
0.2756
3.487414444
3.4874
ENTER
74
COS
COS
74
ENTER
74
TAN
TAN
74
ENTER
TRIGONOMETRIC IDENTITIES

A trigonometric identity
is an equation involving
trigonometric ratios that
is true for all acute
triangles. You are
asked to prove the
following identities in
Exercises 47 and 52.
(sin A)2 + (cos A)2 = 1
sin A
cos A
tan A =
B
c
A
a
b
C