Hello, everyone:

Question

I am working on finding the exact values of angles that are less common and are therefor not found easily on the Unit Circle (at least, they are not labeled). For example, the problem I am asking about is:

10) Find the exact values of the Sine, Cosine and Tangent of 255°. We are supposed to use common angles to assist in our answers (for example, 255° = 300°-45°), and use formulas provided to solve them. I can get sine and cosine alright, but the tangent equation is causing a massive migraine:

tan(x-y) = (tan(x)-tan(y))/(1+tan(x)tan(y))

Using the formula, I get this result:

tan(300-45)=(tan(300)-tan(45))/(1+tan(300)tan(45))

Here is where I am stuck. Problem is, I did not understand the example in the notes, and the book's examples have virtually nothing to do with the actual exercise problems. So, I am trying to deduce this by logic. The denominator appears to be a conjugate, so I tried multiplying by (1-tan(300)tan(45)), and got this result:

[tan(300)+tan^2(300)tan(45)-tan(45)-tan(300)tan^2(45)]/(1-tan^2(300)tan^2(45))

Besides being nightmarishly complex, it also appears to be a dead end. I would appreciate it, greatly, if someone could take their time and slowly explain how to do this portion of my assignment?

With kind regards (except for my math teacher),

Timothy

Answer 1

First of all, I would not have used
225 = 300 - 45 but rather

225 = 180 + 45 and then use

tan(x+y) = (tanx + tany)/(1 - tanxtany)

you should know that tan45 = 1 and tan 180 = 0

so tan 225
= tan (180+45)
= (tan180+tan45)/(1-tan180tan45)
= 1/(1=0)
= 1

check with a calculator.

try to use combinations that involve angles like 0,30,45,60,90, 180 and 360

to use 300 would mean that you would first of all have to calculate tan 300 as a preliminary problem

Answer 2

Tim,

This can be done very easily by BASICS of Tangent function:

Tan has a period of PI, which is 180 degree.

When you have a angle like 225, all you need to do is add or subtract multiples of 180(in this case, 150 itself) to get a common angle:

225-180 = 45

Tan(45)=1, since 225 is in Quadrant III,
it is positive, so final answer(the whole procedure) is

tan(225)=tan(225-180)=tan(45)=1

Contact me for email help

Answer 3

replace 150(in the parenthesis) by 180 in my last post, that was a typo.