Trig Identities: Using Tan Theta and Sine Squared Theta plus Cos Squared Theta

The video tutorial covers fundamental trigonometric identities, including the Pythagorean identity and the relationship between sine, cosine, and tangent. It explains how to derive these identities using basic trigonometric ratios and Pythagoras' theorem. The tutorial then demonstrates how to apply these identities to solve trigonometric equations, including quadratic equations, using examples and step-by-step solutions.

What is the relationship between tan(Theta), sin(Theta), and cos(Theta)?

• tan(Theta) = cos(Theta)/sin(Theta)

• tan(Theta) = sin(Theta)/cos(Theta)

• tan(Theta) = 1/(sin(Theta) * cos(Theta))

• tan(Theta) = sin(Theta) * cos(Theta)

Which identity is derived using Pythagoras' theorem?

• tan^2(Theta) + 1 = sec^2(Theta)

• sin(Theta) * cos(Theta) = 1

• sin^2(Theta) + cos^2(Theta) = 1

• 1 + cot^2(Theta) = csc^2(Theta)

In solving 3sin(Theta) = 4cos(Theta), what is the first step?

• Multiply both sides by sin(Theta)

• Add sin(Theta) to both sides

• Divide both sides by cos(Theta)

• Subtract cos(Theta) from both sides

What is the CAST diagram used for?

• To calculate the exact value of trigonometric functions

• To determine the sign of trigonometric functions in different quadrants

• To solve quadratic equations

• To find the hypotenuse of a triangle

How do you express sin^2(Theta) in terms of cos^2(Theta)?

• sin^2(Theta) = 1 - cos^2(Theta)

• sin^2(Theta) = cos^2(Theta) - 1

• sin^2(Theta) = 1 + cos^2(Theta)

• sin^2(Theta) = 2cos^2(Theta)

What is the quadratic formula used for in trigonometric equations?

• To determine the period of trigonometric functions

• To find the hypotenuse of a triangle

• To solve equations involving sin(Theta) and cos(Theta)

• To solve quadratic equations in terms of trigonometric functions

What are the solutions for cos(Theta) when using the quadratic formula?

• Theta = 90 and 270 degrees

• Theta = 45 and 135 degrees

• Theta = 38.7 and 321.3 degrees

• Theta = 0 and 180 degrees