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**Unformatted text preview: **al side of an angle θ (plotted in
standard position) which lies on the circle of radius r, x2 + y 2 = r2 . Then:
• sec(θ) = r
=
x x2 + y 2
, provided x = 0.
x • csc(θ) = r
=
y x2 + y 2
, provided y = 0.
y y
, provided x = 0.
x
x
• cot(θ) = , provided y = 0.
y • tan(θ) = Example 10.3.4.
1. Suppose the terminal side of θ, when plotted in standard position, contains the point Q(3, −4).
Find the values of the six circular functions of θ.
2. Suppose θ is a Quadrant IV angle with cot(θ) = −4. Find the values of the ﬁve remaining
circular functions of θ.
Solution.
√
1. Since x = 3 and y = −4, r = x2 + y 2 = (3)2 + (−4)2 = 25 = 5. Theorem 10.9 tells us
cos(θ) = 3 , sin(θ) = − 4 , sec(θ) = 5 , csc(θ) = − 5 , tan(θ) = − 4 , and cot(θ) = − 3 .
5
5
3
4
3
4 644 Foundations of Trigonometry 2. In order to use Theorem 10.9, we need to ﬁnd a point Q(x, y ) which lies on the terminal side
of θ, when θ is plotted in standard position. We have that cot(θ) = −4 = x , and since θ is a
y
4
Qu...

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