Trigonometry

Hello, everyone:

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

  1. 0
  2. 0
  3. 11
asked by Timothy
  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

    1. 0
    2. 0
    posted by Reiny
  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

    1. 0
    2. 0
    posted by Qun
  3. replace 150(in the parenthesis) by 180 in my last post, that was a typo.

    1. 0
    2. 0
    posted by Qun

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig

    Find two standard position primary angles in radians by solving for the unknown. "Primary angles" are those angles which exist between 0 and 2pi. As usual, use exact values in your calculations. cotx + 1 = 0
  2. trig

    Find two standard position primary angles in radians by solving for the unknown. "Primary angles" are those angles which exist between 0 and 2pi. As usual, use exact values in your calculations. cosx - 2cos^2x = 0
  3. Trigononometry and plaine sperical

    Find the exact values of the six trigonometric functions for each of the following angles.draw the angles in standard position 1.300 degree
  4. Math

    1. Two angles whose sides are opposite rays are called _____ angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called ____ angles. A. Adjacent; vertical B. adjacent; complementary
  5. calculus

    g(x)=(x^3)-(3x^2)+17 a)find and classify all critical points of g(x) using exact with x and y values. b)for what values of x is the function concave down; again exact x and y values.
  6. math plz help!!!!!!

    What do angles, acute angles, and complementary angles have in common??? they are all angles duh! my teacher said that that's too obvious Please check your book for the similarities. This site also has several explanations about
  7. Math (pre-celc 12)

    Solve this algebraically for the exact values (Meaning find the x-intercepts): (1/x)=x/(3x+18) I'm not sure what to write as the common denominator. I thought it was: 4x+18 because (3x+x+18)=(4x+18), but I'm not sure what to do
  8. Geometry(High School)

    How could you model two angles with a common vertex and a common side that are not adjacent angles?
  9. algebra

    Evaluate the logarithmic equation for three values of x that are greater than 2, three values of x that are between 1 and 2, and at x=2. y = -log(sub)3 (x - 1) I don't know if I did this right, I changed it to -3^y=x-1. I am
  10. 7th grade math please help Ms. Sue ASAP

    14. Find the value of the missing angle. (It is a hexagon. In the picture, going counter-clockwise, the angles are: 152, 85, 125, 135, 85, and "x" degree angles) 720º 120º 128º 138º I need help finding "x"! So far, the angles

More Similar Questions