Download Trigonometry #1

Trigonometry #1
Distance Formula, (Degrees,Minutes,Seconds),
Coterminal Angles, Trig Function Values
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
2
For finding the distance between two points
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
Ex 1: Find the distance between the points (-7,2) & (3,-8)
2
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
Ex 2: Find the distance between the points (3,5) & (2,12)
5 2
2
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
Ex3: Find the distance between the points
(4 +
) (
2
3, 2 3 & 2 + 3, 2 3
)
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
2
Ex4: Find the value of y so that the distance between the points is 5.
(5,y) & (8,-1)
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
2
Ex4: Find the value of x so that the distance between the points is 17.
(x,11) & (5,-4)
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
2
Ex5: Do the points form vertices of a right triangle? Show Your Work
A(-9,-2), B(-1,-2), C(-9,-11)
Distance Formula
d = (x2 - x1 ) + (y2 - y1 )
2
2
Ex5: Do the points form vertices of a right triangle? Show Your Work
A(-8,-4), B(-1,-2), C(-7,-11)
Degrees,Minutes,Seconds
1 Degree° = 60 Minutes’
1 Minute’ = 60 Seconds”
Ex1: Add the degrees and minutes
51° 29’ + 32°46’
Ex1: Add the degrees and minutes
90° - 73°12’
84°15’
16°48’
Conversions
Convert 34.817° to degrees, minutes, and seconds.
Conversions
Convert 74° 8’ 14” to decimal degrees.
Conversions Practice
To Deg,Min,Sec
a) 122.6853°
b) 89.9004°
To Decimal Degrees
c) 274° 18’ 59”
d) 165° 51’ 9”
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Find 3 angles coterminal to the following:
a) 34°
a) 123°
b) -279°
c) -106°
Coterminal Angles
Coterminal Angles
Find the smallest posititve angle coterminal to
the following:
a) 623°
a) 1023°
b) -279°
c) -106°
Trigonometric Values
 SOH CAH TOA
Sin = Opp/Hyp
Csc = Hyp/Opp
Cos = Adj/Hyp
Sec = Hyp/Adj
Tan = Opp/Adj
Cot = Adj/Opp
Sin = y/r
Csc = r/y
Cos = x/r
Sec = r/x
Tan = y/x
Cot = x/y
Trigonometric Values
Find the 6 trig function values at the point (3,-4)
Trigonometric Values
Find the 6 trig function values at the points:
a) (-4,5)
b) (2,5)
c) (-3,-10)
Trigonometric Values
 Find all 6 trig function values given the equation
3x-y = 0, x>0
Start out by choosing a convenient value for x.
Trigonometric Values
 Find all 6 trig function values given the following
equations:
a) 2x-5y = 0, x<0
b) 3x+7y =0, x>0