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
1 radian = 180o
i) convert 110o to radians
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
in quadrant II.
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
quadrant ___
sign is ___
sec𝜃 =
5𝜋
4
quadrant ___
sign is ___
ii) Determine the measure of all angles that satisfy the following conditions. Round your
answers to the nearest degree.
𝑡𝑎𝑛𝜃 = −3.078 in the domain 0 ≤ 𝜃 ≤ 720𝑜
iii) Determine the measure of all angles that satisfy the following conditions. Give exact
answers.
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.