# PreCalculus 30 Review of Unit Circle ```PreCalculus 30 Review of Unit Circle (4.1, 4.2, 4.3)
4.1 Angles and Angle Measure
a) Positive and Negative Angles
b) Angle Measure
ii) convert 3.5 to degrees
c) Arc Length
𝑎 = 𝜃𝑟
i) Find the arc length in the following diagram.
4.2 The Unit Circle
a)
𝑥2 + 𝑦2 = 1
√7
1
i) Is ( 2 , − 7) on the unit circle?
5
ii) Determine the missing coordinate for the point (𝑥, 13) on the unit circle. The point is
b) EXACT values on the Unit Circle
4.3 Trig Ratios
a) Primary Trig Ratios
𝑦
𝑟
𝑥
𝑐𝑜𝑠𝜃 =
𝑟
𝑦
𝑡𝑎𝑛𝜃 =
𝑥
𝑠𝑖𝑛𝜃 =
𝑠𝑖𝑛𝜃 = 𝑦
𝑐𝑜𝑠𝜃 = 𝑥
𝑡𝑎𝑛𝜃 =
b) Reciprocal Trig Ratios
c) CAST Rule
𝑐𝑠𝑐𝜃 =
1
𝑠𝑖𝑛𝜃
𝑠𝑒𝑐𝜃 =
1
𝑐𝑜𝑠𝜃
𝑡𝑎𝑛𝜃 =
1
𝑡𝑎𝑛𝜃
𝑦 𝑠𝑖𝑛𝜃
=
𝑥 𝑐𝑜𝑠𝜃
i) Without using a calculator, determine the sign (+ or -) of each of the following.
sin 580o
sign is ___
sec𝜃 =
5𝜋
4
sign is ___
ii) Determine the measure of all angles that satisfy the following conditions. Round your
𝑡𝑎𝑛𝜃 = −3.078 in the domain 0 ≤ 𝜃 ≤ 720𝑜
iii) Determine the measure of all angles that satisfy the following conditions. Give exact
𝑠𝑖𝑛𝜃 = −
√3
2
in the domain −𝜋 ≤ 𝜃 ≤ 2𝜋
iv) Determine the value of the five other trigonometric ratios if
𝑐𝑠𝑐𝜃 =
5
, 90𝑜 ≤ 𝜃 ≤ 1800 .
3
v) The point D(-5, -12) lies on the terminal arm of an angle θ in standard position. What
is the exact value of each trigonometric ratio for θ?
Assignment
Page 201
10, 12, 14, 16.
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