Name: ________________________ Class: ___________________ Date: __________
Algebra III: 7.5 and Chapter 9 Study Guide
Short Answer
3 for 0° ≤ x ≤ 180°.
1. Solve 5tanx = 5
2. Solve 2 − 3cos x = 5 + 3cos x for 0° ≤ x ≤ 180°.
3. Solve tanx = cot x for 0 ≤ x ≤ π.
4. Solve tanx sec x − 2tanx = 0 for all real values of x.
5. Solve cos θ ≥
3
2
for 0 ≤ θ ≤ 2π.
6. Name the polar coordinates of the point graphed below.
7. Find the distance between P 1 ÊÁ 4, 16° ˆ˜ and P 2 ÊÁ −2, 177° ˆ˜ on the polar plane.
¯
Ë
¯
Ë
8. Graph the polar equation r = 3 + 3 sinθ .
9. Find the polar coordinates of ( 6
3 , 6) for r > 0.
10. Find the rectangular coordinates of ÊÁ 5, 150° ˆ˜ .
Ë
¯
2
2
11. Write the rectangular equation (x + 7) + y = 49 in polar form.
12. Write the polar equation in rectangular form.
r = −16sin θ
13. Solve sinx + 2 sinx cos x for 0° ≤ x ≤ 180°.
14. Solve cot x + 2cot x sinx for 0° ≤ x ≤ 180°.
2
15. Solve 4cos x − 3 = 0 for all real values of x.
16. Solve
tan 2 x
2
− 2cos 2 x = 1 for 0 ≤ x ≤ 2π .
1
ID: A
Name: ________________________
17. Solve
ID: A
3 tan θ < −1 for 0 ≤ θ ≤ 2π .
ÊÁ 7π ˆ˜
Á
˜˜
˜
18. Graph the point that has polar coordinates ÁÁÁ 2,
ÁÁ 6 ˜˜˜ .
Ë
¯
19. Graph the polar equation θ =
2π
3
.
20. Find the distance between P 1 (4, −
15
180
π ) and P 2 (6, −
π ) on the polar plane.
11
299
2
Name: ________________________
ID: A
21. Graph the polar equation r = 3 − 2 sinθ .
22. Find the polar coordinates of (–6, 6
3 ) for r > 0.
23. Find the rectangular coordinates of ÊÁ 5, 30° ˆ˜ .
Ë
¯
24. Write the rectangular equation in polar form.
2
(x + 2) + y 2 = 4
25. Write the polar equation in rectangular form.
r = 6cos θ
3
ID: A
Algebra III: 7.5 and Chapter 9 Study Guide
Answer Section
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7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
9-1.1 Graph points in polar coordinates.
9-1.3 Determine the distance between two points with polar coordinates.
9-2.1 Graph polar equations.
9-3.1 Convert from rectangular coordinates to polar coordinates.
9-3.2 Convert from polar coordinates to rectangular coordinates.
9-3.3 Write rectangular equations in polar form.
9-3.4 Write polar equations in rectangular form.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
7-5.1 Solve trigonometric equations and inequalities.
9-1.1 Graph points in polar coordinates.
9-1.2 Graph simple polar equations.
9-1.3 Determine the distance between two points with polar coordinates.
9-2.1 Graph polar equations.
9-3.1 Convert from rectangular coordinates to polar coordinates.
9-3.2 Convert from polar coordinates to rectangular coordinates.
9-3.3 Write rectangular equations in polar form.
9-3.4 Write polar equations in rectangular form.
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