Trigonometric Functions and Identities

The video tutorial covers solving trigonometric equations, focusing on simplifying functions using identities, verifying identities, and solving equations through various methods. It explains general solutions and specified intervals, and demonstrates factoring techniques for solving equations. The tutorial concludes with practice recommendations to improve understanding.

What does the expression tangent(π/2 - x) simplify to using co-function identities?

• Sine of x

• Cosine of x

• Cotangent of x

• Secant of x

Which identity is used to simplify secant(θ) * cosine(θ)?

• Pythagorean identity

• Co-function identity

• Reciprocal identity

• Odd-even identity

When solving a linear trigonometric equation, what is the first step?

• Add or subtract terms to isolate the variable

• Multiply both sides by a constant

• Use the quadratic formula

• Apply a trigonometric identity

What is the period of the sine function?

• π/2

• 4π

• π

• 2π

How do you express the general solution for sine(x) = 1?

• x = π/2 + 2πn

• x = π/2 + πn

• x = π/4 + πn

• x = π/4 + 2πn

What is the general solution for tangent(x) = -1?

• x = -π/4 + πn

• x = π/4 + 2πn

• x = -π/4 + 2πn

• x = π/4 + πn

In which quadrants is the tangent function positive?

• Quadrants III and IV

• Quadrants I and III

• Quadrants I and II

• Quadrants II and III

What is the first step in solving a trigonometric equation using factoring?

• Use the quadratic formula

• Set the equation to zero

• Convert all terms to sine and cosine

• Apply a Pythagorean identity

Which identity can be used to express sine squared in terms of cosine squared?

• Odd-even identity

• Reciprocal identity

• Pythagorean identity

• Sine squared identity

What is the simplified form of sine(x) when sine squared(x) = 1/2?

• ±1

• ±1/2

• ±√3/2

• ±√2/2