Trigonometric Identities and Values

This video tutorial covers the use of trigonometric identities to convert products to sums and sums to products. It explains the derivation of these identities and demonstrates their application through various problems, including finding exact values of trigonometric expressions. The lesson concludes with a final problem that reinforces the concepts taught.

What is the primary goal of using trigonometric identities in this lesson?

• To understand geometry

• To learn about calculus

• To rewrite trigonometric expressions and determine function values

• To solve algebraic equations

Which identity is used to rewrite the product of sine -4θ and sine 8θ as a sum?

• First identity for cosine

• Second identity for sine

• Third identity for tangent

• Fourth identity for secant

When rewriting 2 x cosine 7T/2 x cosine 3T/2 as a sum, what is the resulting expression?

• Cosine of 10T

• Cosine of 5T and 2T

• Tangent of 5T and 2T

• Sine of 5T and 2T

What is the exact value of sine A x cosine B when A = 7π/8 and B = 1π/8?

• Square root of 2/2

• Square root of 3/4

• Square root of 2/4

• Square root of 3/2

What is the purpose of sum-to-product identities?

• To convert sums into products

• To convert products into sums

• To solve quadratic equations

• To find derivatives

How is the sum of cosine A + cosine B rewritten using sum-to-product identities?

• As a product of sine and cosine

• As a product of two cosine functions

• As a single cosine function

• As a sum of sine functions

What is the exact value of sine 17π/12 - sine 13π/12 using sum-to-product identities?

• Square root 2/2

• Square root 3/2

• -Square root 2/2

• -Square root 3/2

What is the reference triangle for 5π/4 in standard position?

• 30-30-120 triangle

• 60-60-60 triangle

• 45-45-90 triangle

• 30-60-90 triangle

What is the cosine of 5π/4?

• 1/Square root 3

• -1/Square root 3

• -1/Square root 2

• 1/Square root 2

What is the sine of π/6?

• Square root 3/2

• 1/Square root 3

• Square root 2/2

• 1/2