MTH117
Week 12
15.1 Trigonometric Functions of Any Angle
Definition:
(?𝑖?𝑒): ?𝑖?𝜃 =
?
?
=
????????
ℎ?????????
(𝑐??𝑖?𝑒): 𝑐??𝜃 =
?
?
=
𝑎??𝑎????
ℎ?????????
(?𝑎?𝑔𝑒??): ?𝑎?𝜃 =
?
?
=
????????
𝑎??𝑎????
(𝑐??𝑒𝑐𝑎??): 𝑐?𝑐𝜃 =
1
??? 𝜃
=
?
?
=
ℎ?????????
????????
(?𝑒𝑐𝑎??): ?𝑒𝑐𝜃 =
1
??? 𝜃
=
?
?
=
ℎ?????????
𝑎??𝑎????
(𝑐??𝑎?𝑔𝑒??): 𝑐??𝜃 =
1
?𝑎? 𝜃
=
?
?
=
𝑎??𝑎????
????????
Example: A point of the terminal side of angle
𝜃
has the coordinates (-3, -5). Write the six
trigonometric functions of
𝜃
to three significant digits.
?
2
+ ?
2
= ?
2
(−3)
2
+ (−5)
2
= ?
2
34 = ?
2
? = √34
?𝑖?𝜃 =
−5
√34
𝑐??𝜃 =
−3
√34
?𝑎?𝜃 =
−5
−3
=
5
3
𝑐?𝑐𝜃 =
√34
−5
?𝑒𝑐𝜃 =
√34
−3
𝑐??𝜃 =
−3
−5
=
3
5
?
?
?
?
?
𝜃
•
(?, ?)

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