How do you solve the equation $$2cos(x) - 4 = 0$$ ?

Rearranging gives $$cos(x) = 2$$ . Since the range of cos(x) is [-1, 1], there are no solutions.

How do you solve the equation $$4sin(θ) + 1 = 3$$ ?

Rearranging gives $$4sin(θ) = 2$$ , so $$sin(θ) = \frac{1}{2}$$ . The solutions in [0, 2π) are $$θ = \frac{π}{6}, \frac{5π}{6}$$ .

How do you solve the equation $$6tan(θ) + 6\text{√}3 = 0$$ ?

Rearranging gives $$tan(θ) = -\text{√}3$$ . The solutions in [0, 2π) are $$θ = \frac{5π}{3}, \frac{2π}{3}$$ .

How do you solve the equation $$1 = 5 - 8cos(θ)$$ ?

Rearranging gives $$8cos(θ) = 4$$ , so $$cos(θ) = \frac{1}{2}$$ . The solutions in [0, 2π) are $$θ = \frac{π}{3}, \frac{5π}{3}$$ .

What is the solution for $$sin(θ) = -1$$ in the interval [0, 2π)?

The solution is $$θ = \frac{3π}{2}$$ .

What is the unit circle and its significance in trigonometry?

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define the sine, cosine, and tangent functions for all real numbers.

What are the key angles in trigonometry and their sine and cosine values?

Key angles include 0, π/6, π/4, π/3, π/2, π, 3π/2, and 2π. Their sine and cosine values are commonly memorized.

What is the sine rule in trigonometry?

The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: $$ \frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)} $$ .

What is the cosine rule in trigonometry?

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles: $$c^2 = a^2 + b^2 - 2ab \times cos(C)$$ .

What is the difference between sine and cosine functions?

Sine and cosine functions are both periodic functions, but sine represents the y-coordinate of a point on the unit circle, while cosine represents the x-coordinate.

Solving Trig Equations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the general form of a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically expressed in the form f(θ) = 0, where f is a trigonometric function.

Tags

CCSS.HSF.TF.B.7

2.

FLASHCARD QUESTION

Front

What is the range of the cosine function?

Back

The range of the cosine function is [-1, 1].

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Tags

CCSS.HSF.TF.A.4

4.

FLASHCARD QUESTION

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π.

Tags

CCSS.HSF.TF.A.4

5.

FLASHCARD QUESTION

Front

What is the tangent function defined as?

Back

Tags

CCSS.HSF.TF.A.2

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

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