Notes: Trigonometric Ratios
Theta ­ θ ­ Greek letter used to represent an acute angle of a triangle
Name the opposite side and the adjacent side of θ of each triangle.
A
Z
Y
θ
θ
C
X
B
Oct 30­5:17 PM
Sine Ratio
length of opposite side
Abbreviation: sin θ =
length of hypotenuse
A
θ
B
C
sin θ =
sin θ =
Oct 30­5:32 PM
1
Cosine Ratio (cos θ)
Definition: cos θ = length of adjacent side
length of hypotenuse
cos θ = cos θ =
Oct 30­5:39 PM
Tangent Ratio
Definition: tan θ = length of opposite side
length of adjacent side
tan θ =
tan θ =
Oct 30­5:46 PM
2
A way to remember the Trig Ratios...
S
O
H
C
A
H
T
O
A
Nov 9­8:03 AM
A
Write each ratio.
1. sin A = sin B =
5
4
2. cos A = cos B =
3. tan A = tan B = C
3
B
Oct 30­5:56 PM
3
Write each ratio.
1. sin A = sin B = 2. cos A = cos B =
3. tan A = tan B = C
6
8
B
10
A
Oct 30­6:01 PM
In the previous problems, what relationships did you find for the trig ratios of the acute angles?
1. For each pair of complementary acute angles in a right triangle, the sine of one angle is the cosine of its complement.
2. For each pair of complementary angles in a right triangle, the tangent of one angle is the reciprocal of the tangent of its complement.
Oct 30­5:21 PM
4
Nov 9­7:45 AM
Nov 9­7:48 AM
5