1
Worksheet 2b
RECALL:
I. 45° − 45° − 90° Triangle:
Note:
𝒆𝒂𝒄𝒉 𝒍𝒆𝒈 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝒆𝒂𝒄𝒉 𝒐𝒕𝒉𝒆𝒓
𝑻𝒉𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = √𝟐 × 𝒍𝒆𝒈
NAME:
II. 30° − 60° − 90° Triangle:
Note:
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 (𝒍𝒂𝒓𝒈𝒆𝒔𝒕 𝒔𝒊𝒅𝒆) = 𝟐 × 𝒔𝒎𝒂𝒍𝒍𝒆𝒔𝒕 𝒔𝒊𝒅𝒆
𝒎𝒆𝒅𝒊𝒖𝒎 𝒔𝒊𝒅𝒆 = √𝟑 × 𝒔𝒎𝒂𝒍𝒍𝒆𝒔𝒕 𝒔𝒊𝒅𝒆
Determine trig function values of an angle 𝜽.
Step 1: Draw 𝜃 in standard position.
Step 2: Pick a point on the terminal side of 𝜃, connect it to the x-axis.
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
2
Show step by step for the following problems. Determine 6 trig function
values of the following angle 𝜃.
1. 𝜃 = 210°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (210° ) =
𝑥
𝑟
=
𝑠𝑖𝑛 210° =
𝑦
𝑟
=
𝑡𝑎𝑛 210° =
𝑦
𝑥
=
𝑐𝑜𝑡 210° =
𝑥
𝑦
=
sec 210° =
𝑟
𝑥
=
csc 210° =
𝑟
𝑦
=
3
2. 𝜃 = 225°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate
triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (225°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
4
3. 𝜃 = 240°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate
triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (240°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
5
4. 𝜃 = 270°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate
triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (270°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
6
5. 𝜃 = 300°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (300°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
7
6. 𝜃 = 315°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (315°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
8
7. 𝜃 = 330°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (330°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
9
8. 𝜃 = 360°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (360°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
10
9. 𝜃 = 690°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (690°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
11
10. 𝜃 = −135°
Step 1: Draw 𝜃 in standard position.
Step 2 : Pick a point on the terminal side of 𝜃, connect it to the x-axis
Step 3: Determine x, y, and r of the point using the properties of an appropriate triangle
Step 4: Use definition of Trig function for 𝜃 to evaluate trig function value of 𝜃
cos (−135°) =
𝑠𝑖𝑛 ( ) =
𝑡𝑎𝑛 ( ) =
𝑐𝑜𝑡 ( ) =
sec ( ) =
csc ( ) =
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