Application of a Sum Formula

"Write cos(arctan 1 + arccos x) as an algebraic expression." So, I understand that I am to use formula for cos(u + v) because it fits the expression, where u = arctan 1 and

v = arccos x. I also know that I must create to right triangles for each of the angles u and v, the reason being that the angles are likely to be different. What I do not understand is why, when the formula is used, we don't evaluate cos(arctan 1) as

cos(pi/4), which then equals 0. In the book, cos(arctan 1) is evaluated as

1/sqroot(2). Perhaps I do not understand inverse trigonometric functions as I thought I did.

Re: Application of a Sum Formula

Quote:

Originally Posted by

**Bashyboy** "Write cos(arctan 1 + arccos x) as an algebraic expression." So, I understand that I am to use formula for cos(u + v) because it fits the expression, where u = arctan 1 and

v = arccos x. I also know that I must create to right triangles for each of the angles u and v, the reason being that the angles are likely to be different. What I do not understand is why, when the formula is used, we don't evaluate cos(arctan 1) as

cos(pi/4), which then equals 0. In the book, cos(arctan 1) is evaluated as

1/sqroot(2). Perhaps I do not understand inverse trigonometric functions as I thought I did.

pi/4 is on the unit circle and its cosine is not 0: .

Re: Application of a Sum Formula

Quote:

Originally Posted by

**Bashyboy** "Write cos(arctan 1 + arccos x) as an algebraic expression." So, I understand that I am to use formula for cos(u + v) because it fits the expression, where u = arctan 1 and

v = arccos x. I also know that I must create to right triangles for each of the angles u and v, the reason being that the angles are likely to be different. What I do not understand is why, when the formula is used, we don't evaluate cos(arctan 1) as cos(pi/4), which then equals 0. In the book, cos(arctan 1) is evaluated as 1/sqroot(2). Perhaps I do not understand inverse trigonometric functions as I thought I did.

This is standard fair:

Re: Application of a Sum Formula

You two are certainly right--and I am grateful for that. Sorry for the imprudent observation on my part.

Re: Application of a Sum Formula

Quote:

Originally Posted by

**Bashyboy** "Write cos(arctan 1 + arccos x) as an algebraic expression." So, I understand that I am to use formula for cos(u + v) because it fits the expression, where u = arctan 1 and

v = arccos x. I also know that I must create to right triangles for each of the angles u and v, the reason being that the angles are likely to be different. What I do not understand is why, when the formula is used, we don't evaluate cos(arctan 1) as

cos(pi/4), which then equals 0. In the book, cos(arctan 1) is evaluated as

1/sqroot(2). Perhaps I do not understand inverse trigonometric functions as I thought I did.

An alternative is to note that

So that means