Download Advanced Math Section 5.3 [Day 2] Name: Notes Feb. 2015 ~Label

Advanced Math
Section 5.3 [Day 2]
Notes
Name:
Feb. 2015
~Label the sides of this 𝟑𝟎° − 𝟔𝟎° − 𝟗𝟎° triangle
60°
30°
Find the six trigonometric functions for a 30° − 60° − 90° triangle.
sin 30° =
csc 30° =
sin 60° =
csc 60° =
cos 30° =
sec 30° =
cos 60° =
sec 60° =
tan 30° =
cot 30° =
tan 60° =
cot 60° =
~Label the sides of this 𝟒𝟓° − 𝟒𝟓° − 𝟗𝟎° triangle.
45°
45°
Find the six trigonometric functions for a 45° − 45° − 90° triangle.
sin 45° =
csc 45° =
cos 45° =
sec 45° =
tan 45° =
cot 45° =
Steps to find exact values of trigonometry values.
1. Draw the angle in standard form (draw the terminal side of the angle as the HYPOTENUSE to a right
triangle).
2. Find the reference angle and place it on the picture.
3. Draw a right triangle to the x-axis and fill in all the angles.
4. Label all the sides – be sure to put negative signs in front of the values of the sides that go to the left or
down. The hypotenuse is always POSITIVE.
5. Evaluate.
Use the reference angle to find the EXACT VALUE of each trigonometric function.
1. sin 45°
2. cos 60°
3. tan 30°
4. sin 210°
5. tan 330°
6. cos 330°
Use the reference angle to find the EXACT VALUE of each trigonometric function.
7. csc 30°
8. sin 240°
9. tan 225°
Let 𝜽 be an angle in standard position. State the quadrant in which the terminal side of 𝜽 lies.
10. sinθ > 0,
cosθ > 0
11. tanθ < 0,
sinθ < 0
12. sinθ < 0,
cosθ > 0
Advanced Math
Section 5.3 [Day 2]
Homework Worksheet
Name:
Feb. 2015
Use the reference angle to find the EXACT VALUE of each trigonometric function.
1. sin 225°
2. cos 300°
3. tan 405°
4. sec 150°
5. csc 240°
6. cot 210°
7. cos 675°
8. tan (− 30°)
9. sec 765°
Use the reference angle to find the EXACT VALUE of each trigonometric function.
10. sin 315°
11. cos 135°
12. csc (−510)°
13. cot 585°
14. cos 570°
15. tan 240°
Let 𝜽 be an angle in standard position. State the quadrant in which the terminal side of 𝜽 lies.
16. cosθ > 0, tanθ < 0
Day 1 ANSWERS:
17. sinθ < 0,
1. −
7.
√2
√2
2
13. 1
2
2.
1
2
8. −
√3
3
√3
14. −
2
cosθ < 0
18. tanθ < 0,
2√3
3. 1
4. −
9. √2
10. −
15. √3
16. IV
3
√2
2
5. −
cosθ < 0
2√3
3
√2
11. −
17. III
2
6. √3
12. −2
18. II
Advanced Math
Section 5.3 [Day 3]
Notes
Name:
Feb. 2015
Without a calculator, find the following exact values.
Hint: Use the answers from yesterday’s notes to help you!!!
1. sin 210° − cos 330° tan 330°
2. tan 225° + sin 240° cos 60°
Find the exact value of each expression.
3. cosθ =
√3
,
2
1
270° < θ < 360°; find tanθ
5. sinθ = − 2 and cosθ = −
√3
2
; find tanθ
1
2
4. sinθ = ,
6. sinθ = −
90° < θ < 180°; find cosθ
√3
,
2
1
cosθ = − 2 ; find cotθ
Advanced Math
Section 5.3 [Day 3]
Homework Worksheet
Name:
Feb. 2015
Without a calculator, find the following exact values.
Hint: Use the answers from yesterday’s notes and homework to help you!!!
1. cos180° sin315° − tan 330°
2. sin 270° tan45° − cos 60°
3. cos315° tan240° + cos210°
4. sin135° + cos135°
Find the exact value of each expression.
1
2
5. sinθ = − ,
180° < θ < 270°; find tanθ
6. cotθ = −1,
7. cscθ = √2,
90° < θ < 180°; find cotθ
8. secθ =
2√3
,
3
90° < θ < 180°; find cosθ
270° < θ < 360°; find sinθ
Find the exact value of each expression.
1
9. sinθ = − 2 and cosθ > 0; find tanθ
11. cosθ =
1
2
10. tanθ = 1 and sinθ < 0; find cosθ
and tanθ = √3 ; find cscθ
12. tanθ = 1 and sinθ =
1
2
14. secθ =
13. cosθ = − and sinθ =
√3
2
; find cotθ
2√3
3
√2
;
2
and sinθ = −
find secθ
1
2
; find cotθ
Day 2 ANSWERS:
1.
8.
3√2 + 2√3
6
1
−2
3
2. − 2
9. −
√3
3
√6 − √3
2
√2
10. − 2
3.
4. 0
11.
2√3
3
5.
√3
3
12. √2
√2
2
√3
−3
6. −
7. −1
13.
14. − √3