Download Document

Refresher: Special Right Triangles
30-60-90
45-45-90
 In a triangle 30°-60°-90° ,
the hypotenuse is twice as
long as the shorter leg, and
the longer leg is 3 times
as long as the shorter leg.
 In a triangle 45°-45°-90° ,
the hypotenuse is 2 times
as long as a leg.
Hypotenuse
Longer 30°
Leg
X 3
2X
45°
Leg
X
Hypotenuse
X 2
45°
60°
X
Shorter Leg
Leg
X
30º
45º
60º
60º
45º
30º
The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
Opp Leg
Sin 
Hyp
Adj Leg
Cos 
Hyp
Opp Leg
Tan 
Adj Leg
hypotenuse
q
adjacent
opposite
opposite
We need a way
to remember
all of these
ratios…
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Old Hippie Apartment
SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj
Example: sin (45º)
Sin =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Sin =
𝑦
1
2
Sin =
Sin =
1
2
2
2
Example: cos (-
7𝜋
)
6
Cos =
Cos =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑥
1
Cos =
− 32
1
Cos =
− 3
2
Find sin θ and cos θ
θ=−
θ = 510º
 Sin (225º) =
1
2
 Cos (225º) = −
𝝅
𝟔
 Sin (−
3
2
 Cos
𝟗𝝅
)
𝟒
=−
𝟗𝝅
(− )
𝟒
=
1
2
3
2
Example: tan (-240º)
Tan =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Tan =
𝑦
𝑥
3
Tan=
2
−1 2
Tan =
Tan =
3
2
×−
2 3
−
2
Tan = −
3
1
Tan = − 3
2
1
Example: tan
13𝜋
( )
4
Tan =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Tan =
Tan=
𝑦
𝑥
− 22
− 22
Tan =
− 2
2
Tan = 1
×
−2
2
Find sin θ, cos θ, and tan θ
θ = 225º
2
 Sin (225º) = −
2
2
 Cos (225º) = −
2
 Tan (225º) = 1
θ=−
𝟗𝝅
𝟒
𝟗𝝅
 Sin (− ) = −
𝟒
𝟗𝝅
 Cos (− ) =
𝟒
𝟗𝝅
 Tan (− ) =
𝟒
2
2
2
2
-1