H Trig: Solving Trig Equations

Front

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

Back

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

Front

What is the double angle formula for sine?

Back

sin(2x) = 2sin(x)cos(x).

Front

How do you solve the equation cot(x)tan(x) = cot(x)?

Back

Factor out cot(x): cot(x)(tan(x) - 1) = 0. Solutions are x = nπ for cot(x) = 0 and x = π/4 + nπ for tan(x) = 1.

Front

What is the range of the sine function?

Back

The range of sin(x) is [-1, 1].

Front

What is the Pythagorean identity involving sine and cosine?

Back

sin²(x) + cos²(x) = 1.

Front

What is the secant function in terms of cosine?

Back

sec(x) = 1/cos(x).

Front

How do you find specific solutions for trigonometric equations on a given interval?

Back

Solve the equation for general solutions, then restrict the solutions to the specified interval.

Front

What is the formula for the tangent of a double angle?

Back

tan(2x) = 2tan(x)/(1 - tan²(x)).

Front

What is the relationship between sine and cosine for complementary angles?

Back

sin(θ) = cos(90° - θ) or sin(θ) = cos(π/2 - θ).

Front

What is the solution for the equation 2sec²(x) + 10tan(x) - 2 = 10tan(x) + 6?

Back

x = π/3, 2π/3, 4π/3, 5π/3.