💕13.3 Solve Trig Equations 1

Front

What is the range of the cosine function?

Back

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

Front

What is the fundamental identity of trigonometry?

Back

The fundamental identity is sin²(x) + cos²(x) = 1.

Front

How do you solve the equation cos(x) + 1 = 0?

Back

To solve cos(x) + 1 = 0, set cos(x) = -1. The solution in the interval [0, 2π) is x = π.

Front

What are the angles where cos(θ) = -√3/2?

Back

The angles are θ = 5π/6 and θ = 7π/6.

Front

How do you simplify the equation cos(x) + √3 = -cos(x)?

Back

Combine like terms to get 2cos(x) = -√3, then solve for cos(x) = -√3/2, leading to angles 150° and 210°.

Front

What is the solution to sin(x) = √3 - sin(x)?

Back

Rearranging gives 2sin(x) = √3, leading to sin(x) = √3/2. The solutions in [0, 2π) are x = π/3 and x = 2π/3.

Front

What is the general solution for sin(θ) = k?

Back

The general solution is θ = arcsin(k) + 2nπ or θ = π - arcsin(k) + 2nπ, where n is any integer.

Front

What is the period of the sine and cosine functions?

Back

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

Front

How do you find the solutions of 2sin(θ) + 3 = 2?

Back

First, isolate sin(θ): 2sin(θ) = -1, so sin(θ) = -1/2. The solutions in [0, 2π) are θ = 7π/6 and θ = 11π/6.

Front

What is the unit circle and how is it used in trigonometry?

Back

The unit circle is a circle with a radius of 1 centered at the origin. It is used to define the sine and cosine of angles based on the coordinates of points on the circle.