What is the general solution for the equation $$3\text{cos}(x) + 1 = 0$$ ?

$$x = \frac{2\text{π}}{3} + 2k\text{π} \text{ or } x = \frac{4\text{π}}{3} + 2k\text{π}, k \text{ in } \text{ℤ}$$ .

What is the general solution for $$\text{cos}(4x) = -1$$ ?

$$x = \frac{(2k+1)\text{π}}{4}, k \text{ in } \text{ℤ}$$ .

Solve the equation $$2\text{sin}(x) = \text{cos}(x)$$ for the general solution.

$$x = \frac{\text{π}}{3} + k\text{π}, k \text{ in } \text{ℤ}$$ .

What is the general solution for $$\text{sin}(3x) = 0$$ ?

$$x = \frac{k\text{π}}{3}, k \text{ in } \text{ℤ}$$ .

Solve the equation $$2\text{sin}(x) - \text{√3} = 0$$ for the general solution.

$$x = \frac{\text{π}}{3} + 2k\text{π} \text{ or } x = \frac{2\text{π}}{3} + 2k\text{π}, k \text{ in } \text{ℤ}$$ .

What is the range of the cosine function?

The range of the cosine function is from -1 to 1, inclusive.

What is the period of the sine function?

The period of the sine function is $$2\text{π}$$ .

What is the period of the cosine function?

The period of the cosine function is $$2\text{π}$$ .

What is the relationship between sine and cosine?

The sine and cosine functions are related by the identity $$\text{sin}^2(x) + \text{cos}^2(x) = 1$$ .

Define the term 'k' in the context of general solutions.

In the context of general solutions, 'k' represents any integer, allowing for the infinite number of solutions that can be generated by adding or subtracting multiples of the period.

What is the general solution for $$\text{sin}(x) = 0$$ ?

$$x = k\text{π}, k \text{ in } \text{ℤ}$$ .

What is the general solution for $$\text{cos}(x) = 0$$ ?

$$x = \frac{\text{π}}{2} + k\text{π}, k \text{ in } \text{ℤ}$$ .

What is the significance of the unit circle in trigonometry?

The unit circle provides a geometric representation of the sine and cosine functions, where the x-coordinate represents cosine and the y-coordinate represents sine for any angle.

Finding General Solutions of Trigonometric Equations Flashcards

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1.

FLASHCARD QUESTION

Front

Define the general solution of a trigonometric equation.

Back

The general solution of a trigonometric equation is a formula that provides all possible angles (solutions) that satisfy the equation, typically expressed in terms of a variable (k) representing any integer.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1, inclusive.

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