Trig Identities and Equations Test

Front

What is the Pythagorean identity in trigonometry?

Back

The Pythagorean identity states that sin²(x) + cos²(x) = 1 for any angle x.

Front

What is the reciprocal identity for sine?

Back

The reciprocal identity for sine states that sin(x) = 1/csc(x).

Front

What is the reciprocal identity for cosine?

Back

The reciprocal identity for cosine states that cos(x) = 1/sec(x).

Front

What is the tangent function in terms of sine and cosine?

Back

The tangent function is defined as tan(x) = sin(x)/cos(x).

Front

How do you solve the equation tan(x) + 1 = 2?

Back

Subtract 1 from both sides to get tan(x) = 1. The solutions in the interval [0, 2π) are x = π/4 and x = 5π/4.

Front

What is the general solution for sin²(x) = 3/4?

Back

The solutions are x = π/3, 2π/3, 4π/3, and 5π/3.

Front

What is the first step to verify the identity tan²(x) + 1 = sec²(x)?

Back

The best first step is to work with the left side and use the Pythagorean identity to change tan²(x).

Front

How do you solve cos(θ) = -√3/2 on the interval [0, 2π)?

Back

The solutions are θ = 5π/6 and θ = 7π/6.

Front

What is the double angle formula for sine?

Back

The double angle formula for sine is sin(2x) = 2sin(x)cos(x).

Front

How do you solve the equation 2sin(x)cos(x) = √2cos(x)?

Back

Factor out cos(x) to get cos(x)(2sin(x) - √2) = 0. The solutions are x = π/4 and x = 3π/4.