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Τριγωνομετρικές εξισώσεις

Authored by Aλέξανδρος Μόσχος

Mathematics

1st - 2nd Grade

Used 11+ times

Τριγωνομετρικές εξισώσεις
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12 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση ημχ =0 έχει λυσεις :

χ = 2κπ

χ = κπ

χ = 2κπ + π

χ = κπ+π2χ\ =\ κ\pi+\frac{\pi}{2}  

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση ημχ = 1 έχει λύσεις της μορφής (κ∈Z)\left(κ\inΖ\right)  

χ = κπ

χ = 2κπ+π2χ\ =\ 2κ\pi+\frac{\pi}{2}  

χ= 2κπ±π2χ=\ 2κ\pi\pm\frac{\pi}{2}  

χ =κπ+π2χ\ =κ\pi+\frac{\pi}{2}  

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση ημχ = 22ημχ\ =\ \frac{\sqrt[]{2}}{2}  έχει λύσεις:

χ = 2κπ±π4χ\ =\ 2κ\pi\pm\frac{\pi}{4}  

χ=2κπ+π4χ=2κ\pi+\frac{\pi}{4}  

χ = κπ +π4χ\ =\ κ\pi\ +\frac{\pi}{4}  

χ = 2κπ+π4 ηˊ χ = 2κπ+3π4χ\ =\ 2κ\pi+\frac{\pi}{4}\ ή\ χ\ =\ 2κ\pi+\frac{3\pi}{4}  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση 2συνχ =1 εˊχει λυˊσεις:2συνχ\ =1\ έχει\ λύσεις:  

χ=2κπ +π3 ηˊ χ =2κπ −π3χ=2κ\pi\ +\frac{\pi}{3}\ ή\ χ\ =2κ\pi\ -\frac{\pi}{3}  

χ= 2κπ±π3χ=\ 2κ\pi\pm\frac{\pi}{3}  

χ=2κπ±π6χ=2κ\pi\pm\frac{\pi}{6}  

χ=2κπ±π4χ=2κ\pi\pm\frac{\pi}{4}  

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση συνχ = 0 έχει λύσεις

χ = κπ

χ=κπ+π2χ=κ\pi+\frac{\pi}{2}  

χ= 2κπ+π2χ=\ 2κ\pi+\frac{\pi}{2}  

χ=κπ2χ=\frac{κ\pi}{2}  

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση 2ημχ + 1 =0 έχει λύσεις:

χ= 2κπ±π6χ=\ 2κ\pi\pm\frac{\pi}{6}  

χ= 2κπ+π6 ηˊ χ = 2κπ +5π6χ=\ 2κ\pi+\frac{\pi}{6}\ ή\ χ\ =\ 2κ\pi\ +\frac{5\pi}{6}  

χ= 2κπ −π6 ηˊ χ = 2κπ +7π6χ=\ 2κ\pi\ -\frac{\pi}{6}\ ή\ χ\ =\ 2κ\pi\ +\frac{7\pi}{6}  

χ = 2κπ+π6 ηˊ χ = 2κπ +7π6χ\ =\ 2κ\pi+\frac{\pi}{6}\ ή\ χ\ =\ 2κ\pi\ +\frac{7\pi}{6}  

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Η εξίσωση συνχ = - −22-\frac{\sqrt[]{2}}{2}  έχει λύσεις:

χ = 2κπ±π4χ\ =\ 2κ\pi\pm\frac{\pi}{4}  

χ = 2κπ±π6χ\ =\ 2κ\pi\pm\frac{\pi}{6}  

χ = 2κπ+π4ηˊ χ = 2κπ+3π4χ\ =\ 2κ\pi+\frac{\pi}{4}ή\ χ\ =\ 2κ\pi+\frac{3\pi}{4}  

χ=2κπ±3π4χ=2κ\pi\pm\frac{3\pi}{4}  

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