# Common Core: High School - Functions : Prove Addition and Subtraction Formula for Trigonometric Functions: CCSS.Math.Content.HSF-TF.C.9

## Example Questions

### Example Question #1 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

To rationalize the denominator multiply the numerator and denominator by the square root of two.

### Example Question #2 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

### Example Question #3 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

### Example Question #4 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

### Example Question #5 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

### Example Question #6 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the subtraction formula for sine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for sine.

Step 3: Substitute in the reference angles into the general addition formula for sine.

Now to rationalize the denominator multiply the numerator and denominator by the square root of two.

### Example Question #7 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the subtraction formula for cosine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for cosine.

Step 3: Substitute in the reference angles into the general addition formula for cosine.

To rationalize the denominator, multiply the numerator and denominator by the square root of two.

### Example Question #8 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for cosine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for cosine.

Step 3: Substitute in the reference angles into the general addition formula for cosine.

To rationalize the denominator multiply the numerator and denominator by the square root of two.

### Example Question #9 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for cosine and special reference angles calculate,

.

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for cosine.

Step 3: Substitute in the reference angles into the general addition formula for cosine.

### Example Question #10 : Prove Addition And Subtraction Formula For Trigonometric Functions: Ccss.Math.Content.Hsf Tf.C.9

Using the addition formula for cosine and special reference angles calculate,

Explanation:

This type of question tests the deep understanding of geometry, right triangles, trigonometry, and dealing with proofs. Questions such as these are not designed to be tested but instead are used to build knowledge that will help in higher level mathematics courses.

For the purpose of Common Core Standards, "prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems", falls within the Cluster C of "prove and apply trigonometric identities" (CCSS.MATH.CONTENT.HSF.TF.C).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Break the angle into two angles that correspond to special reference angles.

Step 2: Write the general addition formula for cosine.

Step 3: Substitute in the reference angles into the general addition formula for cosine.

To rationalize the denominator, multiply by the square root of two.