Download Lesson 1 sine, cosine and tangent ratios Student

Foundations to
college algebra
Trigonometry
Right Triangle
Trig
Lesson 1 Objective:
I will learn the definition of trigonometry, learn the
ratios of
, cosine and
.
1
Definitions
is the study of relationships among
the angles and sides of a right triangle.
Trigonometric
the
is the fraction that compares
of a right triangle.
Trigonometric
is the specific rule
(combination of sides) given by the ratio. There
are a total of 6 trig functions: sine, cosine,
tangent, cosecant, secant and cotangent.
2
Each Trig function has a unique ratio of
Today we will focus on the three on the left.
sin θ = opp
hyp
csc θ = hyp
opp
cos θ = adj
hyp
sec θ = hyp
adj
tan θ = opp
adj
cot θ = adj
opp
An easy acronym
for this side is:
.
this side is ALWAYS
the reciprocal of the
function on the left
3
Write the trig ratios of sin, cos and tan for each of the
acute angle of the right triangle. Include the formula
for each function and simplify all radicals. No decimals
6
8
sin B =
B
A
10
sin A =
cos B =
cos A =
tan B =
tan A =
4
Write the trig ratios of sin, cos and tan for each of the
acute angle of the right triangle. Include the formula
for each function and simplify all radicals. No decimals
A
sin A =
sin B =
cos A =
cos B =
tan A =
tan B =
3 3
6
3
B
5
Write the trig ratios of sin, cos and tan for each of the
acute angle of the right triangle. Include the formula
for each function and simplify all radicals. No decimals
sin B =
B
4
sin A =
4 2
4
cos B =
A
cos A =
tan A =
tan B =
6
Find the missing side then write the trig ratios of sin, cos
and tan for each of the acute angles. Include the formula
and simplify all radicals.
5
θ
β
1. Use
a2 + b2 = c2
to find missing side.
2. Label hyp., opp, adj
13
3. Write the 3 trig ratios:
sin θ = o
sin β = o
h
h
cos θ = a
h
cos β = a
h
tan θ = o
a
tan β = o
a
7
Find the missing side then write the trig ratios of sin, cos
and tan for each of the acute angles. Include the formula
and simplify all radicals.
12
1. Use a2 + b2 = c2
β
θ
to find missing side.
8
2. Label hyp., opp, adj
3. Write the 3 trig ratios:
sin θ = o
sin β = o
h
h
cos θ = a
h
cos β = a
h
tan θ = o
a
tan β = o
a
8
Find the missing side then write the trig ratios of sin, cos
and tan for each of the acute angles. Include the formula
and simplify all radicals.
17
1. Use a2 + b2 = c2
θ
β
to find missing side.
15
2. Label hyp., opp, adj
3. Write the 3 trig ratios:
sin θ = o
sin β = o
h
h
cos θ = a
h
cos β = a
h
tan θ = o
a
tan β = o
a
9
In a right triangle θ and β are acute. Find the
sin θ, tanθ, sin β, cos β and tan β if cos θ = 3
7
1. Draw a pic. Label known sides.
β
θ
2
2
2
2. Find missing side a +b = c
3. Write the trig functions. Simplify
sin θ = o
sin β = o
h
h
cos θ = a
cos β = a
h
h
tan θ = o
tan β = o
a
a
10
In a right triangle θ and β are acute. Find sin θ,
cos θ, sin β, cos β and tan β if tan θ = 7
12
1. Draw a pic. Label known sides.
2. Find missing side:
a2
+
b2
=
c2
β
θ
3. Write the trig functions. simplify
sin θ = o
h
sin β = o
h
cos θ = a
h
cos β = a
h
tan θ = o
a
tan β = o
a
11
Homework
Trigonometry of Right Triangles Lesson 1-18 all.
Write 5 times each on paper
a. Pythagorean Theorem
b. sine ratio
c. Cosine ratio
d. tangent ratio
e. SohCahToa
12