| MATHEMATICS |
WISKUNDE |
| GRADE 11 |
GRAAD 11 |
| MORE EXERCISES |
NOG OEFENINGE |
| Solving trigonometric equations. |
Oplossing van trigonometriese |
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vergelykings. |
| 1. |
Find the general solution for each equation. |
1. |
Bepaal die algemene oplossing vir |
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elke vergelyking. |
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1.1
sin θ = 0,819
1.2
cos α = 0,337
1.3
tan θ = 2,605
1.4
sin α = − 0,468
1.5
cos Φ = − 0,888
1.6
tan α = − 0,43
1.7
cosec α = 2,103
1.8
sec Φ = 1,257
1.9
cot θ = − 0,315
3
1
3
1.10
— tan α = 1,077
1.11
— cos θ = − 0,468
1.12
— sin θ = 0,544
2
2
2
1.13
sin (α + 12,5°) = 0,819
1.14
cos (θ − 22,3°) = − 0,273
1.15
tan (θ − 32,6°) = 2,836
1.16
cot (α + 34,5°) + 1,664 = 0
1.17
2 cosec (θ − 18,3°) = 4,822
1.18
tan (2θ − 28,4°) = − 0,430
| 2. |
Solve the following equations for the |
2. |
Los die volgende vergelykings op |
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given interval : |
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in die gegewe interval : |
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2.1
1,5 tan (θ − 10°) + 1,077 = 0 and // en θ ∈ [0° ; 180°]
2.2
cos 2α = sin 12° and // en θ ∈ [0° ; 90°]
2.3
4 sin (θ − 15°) + 2 = 0 and // en θ ∈ [0° ; 270°]
2.4
sec (2 Φ + 24,3°) − 2,5 = 0 and // en θ ∈ [− 90° ; 90°]
2.5
tan θ − 1 = − 6 and // en θ ∈ [− 180° ; 180°]
2.6
cot (Φ − 11,8°) = − 1,664 and // en θ ∈ [− 90° ; 270°]
| 3. |
Solve the following equations without |
3. |
Los die volgende vergelykings op sonder die |
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using a calculator in the interval [0° ; 360°] : |
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gebruik van 'n sakrekenaar in die |
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interval [0° ; 360°] : |
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3.1
sin (2θ − 40°) + 0,5 = 0
3.2
√2 cos (α + 34°) = 1
3.3
√3 cosec (θ − 14°) = 2
3.4
cot (2α − 18°) = √3
3.5
2 sec (5 θ + 15°) + 1 = 5
3.6
2 cos (2α − 15°) = tan 45°
| 4. |
Solve the following equations : |
4. |
Los die volgende vergelykings op : |
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4.1
sin x . (2 cos x − 1) = 0
4.2
sin x = cos 48°
4.3
cos2 x + sin x = 1
4.4
3 cos2 x − 5 sin x = 1