All Trigonometry Resources
Example Questions
Example Question #1 : Sum, Difference, And Product Identities
True or false:
.
False
True
Cannot be determined
False
The sum of sines is given by the formula .
Example Question #2 : Sum, Difference, And Product Identities
True or false: .
True
False
Cannot be determined
False
The difference of sines is given by the formula .
Example Question #3 : Sum, Difference, And Product Identities
True or false: .
False
True
Cannot be determined
False
The sum of cosines is given by the formula .
Example Question #4 : Sum, Difference, And Product Identities
True or false: .
False
True
Cannot be determined
False
The difference of cosines is given by the formula .
Example Question #5 : Sum, Difference, And Product Identities
Which of the following correctly demonstrates the compound angle formula?
The compound angle formula for sines states that .
Example Question #6 : Sum, Difference, And Product Identities
Which of the following correctly demonstrates the compound angle formula?
The compound angle formula for cosines states that .
Example Question #7 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines
Simplify by applying the compound angle formula:
Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that and
, substitution yields the following:
This is the formula for the product of sine and cosine, .
Example Question #8 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines
Simplify by applying the compound angle formula:
Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that and
, substitution yields the following:
This is the formula for the product of two cosines, .
Example Question #9 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines
Using and the formula for the sum of two sines, rewrite the sum of cosine and sine:
Substitute for
:
Apply the formula for the sum of two sines, :
Example Question #10 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines
Using and the formula for the difference of two sines, rewrite the difference of cosine and sine:
Substitute for
:
Apply the formula for the difference of two sines, .
Certified Tutor
All Trigonometry Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)