Transcript Document

Quiz 1 Need-to-Know
Arithmetic Mean (AM) or average: (a + b) / 2
Geometric Mean (GM): √ab
a
Altitude = GM of divided hypotenuse
b
alt = √ab
Pythagorean Theorem:
a2 + b2 = c2
Pythagorean Triples: Whole numbers that solve the theorem
45
6
Side opposite 30° angle is ½ the hypotenuse
Side opposite 45° angle is ½ the hypotenuse times √2
Side opposite 60° angle is ½ the hypotenuse times √3
6
45
3√2
30
60
3
Transparency 7-4
5-Minute Check on Lesson 7-3
Find x and y.
1.
x = 16
32
x = 5√2
2.
x
10
y = 16√3
30°
y°
x
y = 45°
y
3. The length of a diagonal of a square is 15√2 cm. Find the perimeter
of the square.
P = 60 cm
4. The side of an equilateral triangle measures 21 inches. Find the
length of the altitude of the triangle. 10.5√3 ≈ 18.19 in
5. ∆MNP is a 45°- 45°- 90° triangle with right angle P. Find the
coordinates of M in quadrant II with P(2,3) and N(2,8).
6.
Standardized Test Practice:
In the right triangle
(-3,3)
C
D
3x°
find CD if DE = 5.?
6x°
A
5
B
5√3
C
(5/3)√3
Click the mouse button or press the
Space Bar to display the answers.
D
10
E
Lesson 7-4a
Right Triangle Trigonometry
Trigonometric Functions
• Main Trig Functions:
– Sine
– Cosine
– Tangent
sin
cos
tan
-1 ≤ range ≤ 1
-1 ≤ range ≤ 1
-∞ ≤ range ≤ ∞
• Others:
– Cosecant
– Secant
– Cotangent
– Tangent
csc
sec
cot
1 / sin
1 / cos
1/ tan
sin / cos
Trig Definitions
• Sin (angle) =
Opposite
---------------Hypotenuse
S-O-H
• Cos (angle) =
Adjacent
---------------Hypotenuse
C-A-H
• Tan (angle) =
Opposite
---------------Adjacent
T-O-A
Ways to Remember
• S-O-H
Some Old Hillbilly
Caught Another Hillbilly
Throwing Old Apples
• C-A-H
• T-O-A
Some Old Hippie
Caught Another Hippie
Tripping On Acid
Extra-credit:
Your saying
Anatomy of a Trig Function
A
Example:
θ
opposite side
BC
sin A = sin θ = ---------------------- = -----hypotenuse
AB
C
B
Use trig functions to help find a missing side in a right triangle.
Format:
Trig Function ( an angle, θ for example) =
some side
----------------------some other side
where the some side or the some other side is the missing side
If θ = 30 and AB = 14, then to find BC we have
opposite side
BC BC
sin θ = sin 30 = 0.5 = ---------------------- = ----- = -----hypotenuse
AB 14
(14) 0.5 = BC = 7
Anatomy of a Trig Function
A
Example:
θ
opposite side
BC
sin A = sin θ = ---------------------- = -----hypotenuse
AB
C
Use inverse trig functions to help find a missing angle in a right ∆.
Format:
Trig Function
-1
B
some side
(-------------------------) = missing angle, θ for example
some other side
where the trig function -1 is found using 2nd key then the trig
function on calculator
If BC = 7 and AB = 14, then to find A or θ we have
opposite side
BC
7
sin θ = ---------------------- = ----- = ----- = 0.5
hypotenuse
AB 14
A = θ = sin-1(0.5) = 30°
Example 1
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
Answer:
Example 2
Find sin A, cos A, tan A, sin B, cos B, and
tan B. Express each ratio as a fraction and
as a decimal.
Answer:
Example 3
Use a calculator to find tan
thousandth.
KEYSTROKES: TAN
56
to the nearest ten
ENTER
1.482560969
Answer:
Use a calculator to find cos
thousandth.
KEYSTROKES: COS
Answer:
90
to the nearest ten
ENTER
0
Example 4
a. Use a calculator to find sin 48° to the nearest ten
thousandth.
Answer:
b. Use a calculator to find cos 85° to the nearest ten
thousandth.
Answer:
Summary & Homework
• Summary:
– Trigonometric ratios can be used to find measures
in right triangles
– Sin of an angle is opposite / hypotenuse
– Cos of an angle is adjacent / hypotenuse
– Tan of an angle is adjacent / hypotenuse
• Homework:
– pg 367-368; 1, 4, 5-8, 11, 15, 16