💕13.3 Solve Trig Equations 1

Front

What is the general solution for the equation tan(x) + 1 = 2?

Back

x = π/4 + nπ, where n is any integer.

Front

What is the solution for the equation 1/4sin(x) + 1 = 0 on the interval [0, 2π)?

Back

No solution.

Front

How do you solve the equation 2sin(θ) + 3 = 2?

Back

The solutions are θ = 7π/6 and θ = 11π/6.

Front

What are the solutions for the equation 4cos²(x) - 3 = 0 on the interval [0, 2π)?

Back

The solutions are x = π/6, 5π/6, 7π/6, and 11π/6.

Front

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

Back

The solutions are x = 150° and x = 210°.

Front

What is the range of the tangent function?

Back

The range of the tangent function is all real numbers.

Front

What is the period of the sine and cosine functions?

Back

The period of sine and cosine functions is 2π.

Front

What is the Pythagorean identity for sine and cosine?

Back

sin²(x) + cos²(x) = 1.

Front

What is the relationship between sine and cosine in a right triangle?

Back

sin(θ) = opposite/hypotenuse and cos(θ) = adjacent/hypotenuse.

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, used to define trigonometric functions for all angles.