Geometry – Kinsey
Unit 9: Right Triangle Trigonometry
Notes 3
SINE AND COSINE RELATIONSHIP
TODAY’S TARGET: I can _____use_____ _____trig_____ _____ratios_____ to _____solve_____ _____problems_____.
EXPLORING SINE AND COSINE
Find the value of each given trig ratio and make note of any patterns you see.
#
sine
cosine
right triangle
observations/patterns
possible observations:
3
4
 same two answers each time, but
sin(37°) =
cos(37°) =
53°
5
in different order
5
5
3
①
 answers are opposite
4
3
 angles add up to 90 for the same
37°
sin(53°) =
cos(53°) =
5
5
ratio
4
②
5
sin(23°) =
13
sin(67°) =
③
8
sin(28°) =
17
sin(62°) =
④
12
13
15
17
7
sin(16°) =
25
sin(74°) =
24
25
12
cos(23°) =
13
cos(67°) =
5
13
15
cos(28°) =
17
cos(62°) =
8
17
24
cos(16°) =
25
cos(74°) =
7
25
13
possible observations:
 same as above
67°
5
23°
12
17
possible observations:
 same as above
62°
8
28°
15
25
possible observations:
 same as above
74°
7
16°
24
SINE AND COSINE RELATIONSHIP
From our exploration we can conclude that…
sin(90 − 𝜃 ) = cos 𝜃
and
cos(90 − 𝜃 ) = sin 𝜃
Example:
Solve for 𝜃.
cos 34° = sin 𝜃
 always subtract from
90
−34
56
90 when comparing
sine and cosine
𝜃 = 56°
the angles of sine and cosine
add up to 90 degrees
On Your Own:
Solve for 𝜃.
sin 56° = cos 𝜃
𝜃 = 34°