Trigonometric Functions of Any Angle Date - Precalculus
PCM 40S - Chapter 2
Name___________________________________
Trigonometric Functions of Any Angle
ID: 1
Date________________
Use the given point on the terminal side of angle ¦È to find the value of the trigonometric
function indicated.
1) tan ¦È ; (3, 4)
2) sec ¦È ; (?2, ?2 3 )
3) cos ¦È ; (2, ? 5 )
4) cot ¦È ; (? 17, 8)
5) sin ¦È ; ( 13, ?6)
6) csc ¦È ; (?4, ?2 5 )
Find the exact value of each trigonometric function.
7) sin ?
3¦Ð
2
8) csc ?
9) cos ?
7¦Ð
6
10) cot
11) tan ?
¦Ð
6
¦Ð
4
4¦Ð
3
12) sec ?
5¦Ð
3
State the quadrant in which ¦È lies.
13) sin¦È < 0 and cos¦È < 0
?t 8KHunttaE jSbolf5tnw7aRr5eA 4LuLCCh.6 9 FAGlwlZ WrjiCgkhItms3 frZelsueOrxvje4d8.D M xMkaWdPeT Awwigtmh0 gIfncfNiCnSi1tUen cAFlqgpePbvrea1 w2k.1
14) sin¦È > 0 and cos¦È > 0
-1-
Worksheet by Kuta Software LLC
15) sin¦È > 0 and tan¦È < 0
16) sec¦È > 0 and cot¦È < 0
Find the values of the six trigonometric functions of ¦È given the constraint on the angle.
15
; sin¦È < 0.
8
3
17) sin¦È = ; ¦È lies in Quadrant II.
5
18) tan¦È = ?
19) cot¦È = ?3; cos¦È > 0.
20) sin¦È = 0; sec¦È = ?1.
Solve each equation for 0 ¡Ü ¦È < 2¦Ð .
21) ?
3
= cos ¦È
2
23) tan ¦È = 0
22) ?
1
= sin ¦È
2
24) sin ¦È = 0
Evaluate without using a calculator. Keep in mind the domain of the inverse function.
25) sin
?1 1
2
27) tan
29) sin
26) cos
?1
?1
3
3
3
2
?y mKpu0tMaO 5SLo5f5tBwWa4rseB 1LgLAC1.D P GATlKlq FrsiEguhntPsE YrdeYsleVrDvteKde.D l vMZabd9e5 9wai2tlh5 dIQnXfliCnOiOtkej vALlOgHenb4rdaS X2l.D
?1 1
2
?1
28) tan ? 3
?1
30) cos ?
-2-
1
2
Worksheet by Kuta Software LLC
Answers to Trigonometric Functions of Any Angle (ID: 1)
1)
2) ?2
4
3
4) ?
17
8
5) ?
7) 1
3)
6
7
3 5
5
3
9) ?
2
12) 2
6) ?
8) ? 2
3
3
13) III
16) II
10)
11) ?
2
3
3
3
14) I
15) II
4
3
5
4
5
17) cos¦È = ? ; tan¦È = ? ; csc¦È = ; sec¦È = ? ; cot¦È = ?
5
4
4
3
3
15
15
17
8
8
17
18) sin¦È = ? ; cos¦È = ; tan¦È = ? ; csc¦È = ? ; sec¦È = ; cot¦È = ?
17
8
15
15
17
8
1
10
10
10
19) sin¦È = ?
; cos¦È = 3 ?
; tan¦È = ? ; csc¦È = ? 10; sec¦È =
; cot¦È = ?3
10
10
3
3
20) sin¦È = 0; cos¦È = ?1; tan¦È = 0; csc¦È is undefined; sec¦È = ?1; cot¦È is undefined
23) {0, ¦Ð }
5¦Ð 7¦Ð
7¦Ð 11¦Ð
,
22)
,
21)
6 6
6
6
24) {0, ¦Ð }
¦Ð
¦Ð
25)
26)
6
3
¦Ð
¦Ð
¦Ð
27)
28) ?
29)
6
3
3
2¦Ð
30)
3
{
}
{
?r wKBuYtkaQ xSQoyfUtIwQawrkeU dLzLsCK.0 5 0AElNlS CriixgyhCtYsL hroeXsVeHrUvqeGdo.P J GMTaIdwen awAiTtrh3 wIInmfqiAnVihtCec 5AQlFgFe9bjrya6 t2L.v
}
-3-
Worksheet by Kuta Software LLC
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