Trigonometric Identities and Functions

This video tutorial covers 15 trigonometry problems for 11th-grade math, focusing on solving equations, calculating trigonometric functions, and applying identities. Each problem is explained step-by-step, providing a comprehensive understanding of trigonometric concepts and their applications.

What is the sum of all solutions for the equation 4cos2x = 2 - 2cos2x within the interval 180° ≤ x ≤ 360°?

• 600

• 810

• 540

• 720

How do you express the equation tan(2x) - tan(5x) / (1 + tan(2x)tan(5x)) = 0 in terms of a single tangent function?

• tan(3x) = 0

• tan(7x) = 0

• tan(5x) = 0

• tan(2x) = 0

What is the value of tan(375°) using angle reduction?

• tan(60°)

• tan(15°)

• tan(45°)

• tan(30°)

Given sin(α) = 2/√5 and cos(β) = 4/5, what is sin(α - β)?

• 4/5√5

• 2/5√5

• 1/5√5

• 3/5√5

What is the simplified form of sin(-15°) - cos(375°)?

• -1/5√6

• -1/2√6

• -1/4√6

• -1/3√6

What is the result of rationalizing the expression involving square roots in trigonometry?

• 1/8

• 1/64

• 1/32

• 1/16

How is the cosine of a double angle calculated using trigonometric identities?

• Using the formula 1 + 2cos^2(x)

• Using the formula sin^2(x) + cos^2(x)

• Using the formula 2cos^2(x) - 1

• Using the formula 1 - 2sin^2(x)

In a right triangle, if cos(A) = 4/5, what is the length of the opposite side if the hypotenuse is 5?

• 6

• 4

• 5

• 3

Which identity is used to simplify the expression sin(A) - sin(B)?

• 2sin((A+B)/2)cos((A-B)/2)

• cos(A)cos(B) - sin(A)sin(B)

• 2cos((A+B)/2)sin((A-B)/2)

• sin(A)cos(B) + cos(A)sin(B)

What is the simplified form of the expression 2sin(alpha - beta) / cos(alpha + beta)?

• tan(alpha) - tan(beta)

• sin(alpha) + sin(beta)

• cos(alpha) - cos(beta)

• tan(alpha) + tan(beta)