Complete the following mathematical questions.
1
Worksheet 2
RECALL:
I. 45° − 45° − 90° Triangle:
Note:
= √ ×
NAME:
II. 30° − 60° − 90° Triangle:
Note:
( ) = ×
= √ ×
Determine trig function values of an angle .
Step 1: Draw in standard position.
Step 2: Pick a point on the terminal side of , 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 to evaluate trig function value of
2
Show step by step for the following problems. Determine 6 trig function
values of the following angle .
1. = 0°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (0°) =
=
0° =
=
0° =
=
0° =
=
sec 0° =
=
csc 0° =
=
3
2. = 30°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (30°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
4
3. = 45°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (45°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
5
4. = 60°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (60°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
6
5. = 90°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (90°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
7
6. = 120°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (120°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
8
7. = 135°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (135°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
9
8. = 150°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (150°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
10
9. = 180°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (180°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
1
Worksheet 2b
RECALL:
I. 45° − 45° − 90° Triangle:
Note:
= √ ×
NAME:
II. 30° − 60° − 90° Triangle:
Note:
( ) = ×
= √ ×
Determine trig function values of an angle .
Step 1: Draw in standard position.
Step 2: Pick a point on the terminal side of , 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 to evaluate trig function value of
2
Show step by step for the following problems. Determine 6 trig function
values of the following angle .
1. = 210°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (210° ) =
=
210° =
=
210° =
=
210° =
=
sec 210° =
=
csc 210° =
=
3
2. = 225°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (225°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
4
3. = 240°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (240°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
5
4. = 270°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (270°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
6
5. = 300°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (300°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
7
6. = 315°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (315°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
8
7. = 330°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (330°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
9
8. = 360°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (360°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
10
9. = 690°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (690°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
11
10. = −135°
Step 1: Draw in standard position.
Step 2 : Pick a point on the terminal side of , 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 to evaluate trig function value of
cos (−135°) =
( ) =
( ) =
( ) =
sec ( ) =
csc ( ) =
Read all directions carefully. Circle or box all final answers.
1. Use the given information to determine which trigonometric function should be used to find . Write an
equation to solve for the missing angle. DO NOT SOLVE.
a. b.
c. d.
2. If = 32,ℎ = 19 and = 41∘, find ∠ .
Math 347 – Skills for Trigonometry
Worksheet – Solving Right Triangles
)
Name _________________________
2.5cm
5cm
7in
4in
5cm
12cm
3ft
4ft
5ft
Read all directions carefully. Circle or box all final answers.
