Solving 1st and 2nd Degree Trigonometric Equations

Front

What is the general form of a 1st degree trigonometric equation?

Back

A 1st degree trigonometric equation is an equation that can be expressed in the form of a trigonometric function equal to a constant, such as sin(θ) = k, cos(θ) = k, or tan(θ) = k.

Front

What is the general form of a 2nd degree trigonometric equation?

Back

A 2nd degree trigonometric equation is an equation that can be expressed in the form of a trigonometric function squared equal to a constant or another trigonometric function, such as sin²(θ) = k or 1 + tan²(θ) = sec²(θ).

Front

What is the range of the secant function?

Back

The range of the secant function, sec(θ), is (-∞, -1] ∪ [1, ∞).

Front

What is the range of the cosecant function?

Back

The range of the cosecant function, csc(θ), is (-∞, -1] ∪ [1, ∞).

Front

How do you solve the equation -1 - 2sec²(θ) = -3sec²(θ)?

Back

Rearranging gives sec²(θ) = 1, leading to θ = 0, π within the interval [0, 2π].

Front

What is the solution to the equation -2 = -5 + 3sec(θ)?

Back

Rearranging gives sec(θ) = 1, leading to θ = 0 within the interval [0, 2π].

Front

Is it true that sin(θ) = -1 has no solutions?

Back

FALSE; sin(θ) = -1 has solutions, specifically θ = 3π/2.

Front

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

Back

Rearranging gives cot(θ) = -1, leading to θ = 3π/4, 7π/4 within the interval [0, 2π].

Front

How do you solve the equation csc(θ) + √2 = 0?

Back

Rearranging gives csc(θ) = -√2, leading to θ = 5π/4, 7π/4 within the interval [0, 2π].

Front

What is the relationship between sec(θ) and cos(θ)?

Back

Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).