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24 questions
1
. Match the right triangle definition with its trigonometric function.
(a)
hyp
adj
=
(b)
opp
adj
=
(c)
opp
hyp
=
(d)
adj
opp
=
(e)
hyp
opp
=
(f)
adj
hyp
=
2
. Fill in the blanks.
Relative to the acute angle θ, the three sides of a right triangle are the , the side, and the side.
3
. Use the figure to answer the question.
What is the length of the side opposite the angle θ?
4. Use the figure to answer the question.
What is the length of the side adjacent to the angle θ?
5. Use the figure to answer the question.
What is the length of the hypotenuse?
6
. Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. Let b = 3 and c = 5.)
|
sin(θ) |
= | ||||||||||||||||||||||||||
|
cos(θ) |
|||||||||||||||||||||||||||
|
tan(θ) |
|||||||||||||||||||||||||||
|
csc(θ) |
|||||||||||||||||||||||||||
|
sec(θ) |
|||||||||||||||||||||||||||
|
cot(θ) |
7. Find the exact values of the six trigonometric functions of the angle θ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
|
sin θ |
||
|
cos θ |
||
|
tan θ |
||
|
csc θ |
||
|
sec θ |
||
|
cot θ |
8
. Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.
cos θ =
| 6 |
| 8 |
9. Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.
csc θ =
|
13 |
|
| 3 |
1
0
. Construct an appropriate triangle to complete the table. (0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)
|
Function |
θ (deg) |
θ (rad) |
Function Value |
||||||||
| cos |
135 ° |
11. Construct an appropriate triangle to complete the table. (0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)
| sec | ° |
π 4 |
12. Construct an appropriate triangle to complete the table. (0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)
| sin | 0 |
13. Complete the identity.
sin θ =
| 1 |
14. Complete the identity.
cos θ =
1
15. Complete the identity.
csc θ =
1
16. Complete the identity.
cot θ =
1
17. Complete the identity.
1 +
tan2 θ =
18. Complete the identity.
sin(90° − θ) =
19. Complete the identity.
cos(90° − θ) =
20. Use the given function values, and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
sin(30°) =
| 2 |
, tan(30°) =
|
3 |
(a) csc(30°) =
(b) cot(60°) =
(c) cos(30°) =
(d) cot(30°) =
21. Use the given function value and the trigonometric identities to find the indicated trigonometric functions.
tan β = 8
(a)
cot β
(b)
cos β
(c) tan(90° − β)
(d) csc β
22. Use trigonometric identities to transform the left side of the equation into the right side (0 < θ < π/2).
|
1 + cos θ 1 − cos θ |
|
sin2 θ |
23. Use trigonometric identities to transform one side of the equation into the other (0 < θ < π/2).
|
tan θ + cot θ tan θ |
tan θ tan θ + cot θ tan θ |
| 1 + | |
|
csc2 θ |
24. Find the values of θ in degrees (0° < θ < 90°) and radians (0 < θ < π/2) without using a calculator.
(a)
tan θ =
3
3
θ = degrees
θ = radians
(b)
cos θ =
1
2
θ = degrees
θ = radians
