MATH

posted by .

FIND THE SOLUTION FOR THE EQUATION. ASSUME THAT ALL ANGLES IN WHICH AN UNKNOWN APPEARS ARE ACUTE ANGLES.

COT ALPHA=TAN( ALPHA +40DEGREES)


HOW DO I SOLVE THIS?

  • MATH -

    I will use A for alpha

    cot A = tan(A + 40)
    1/tanA = (tanA + tan40)/(1 - tan^2A)
    let tanA = x

    1/x = (x + .8391)/(1-x(.8391))
    x^2 + .8391x = 1 - .8391x
    x^2 + 1.6782x - 1 = 0
    by the formula
    x = (-1.6782 ± √6.816355)/2 = .4663 or -2.1445

    so tanA = .4663, then A = 25° or 205°
    if tanA = -2.1445 , A = 115° or 295°

    I will check the 205°
    LS = cot 205° = 2.1445
    RS = tan(205+40) = tan 245 = 2.1445
    YEAHHH!

    I will let you check the others.

  • MATH -

    Just came back from a walk, and I kept thinking about this question and why the answer came out to rather exact values of the angle.
    Then I realized that I could have used the complementary angle property, that is,
    cot A = tan(90°-A)

    so in
    cotA = tan(A+40)
    tan(90-A) = tan(A+40)
    so obviously
    90-A = A + 40
    50 = 2A

    A = 25 !!!!!!!!!!!!

    and of course since tanA = tan(180-A)
    A is also equal to 180-25 = 115°

    and since the period of tanA is 90° , adding or subtracting multiples of 90 would yield more answers
    so 25+90 = 115
    115+90 = 205
    205+90 = 295

    which is the same answer as the complicated solution I had before.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. ALGEBRA 1

    If x and 3x-10 represent the measure of the acute angles of a right tringle find the value of x. THANKS Let's take it step by step. A triangle has 3 angles in it. Those three angles, when added together, is 180. In a right triangle, …
  2. trig

    Solve for the unknown. Assume that all of the angles are acute. 1. U = 69 A = 75 AN = 56 NU = ______ is this right NU= 92.05
  3. maths (trigonometry)

    sin(alpha-bita)=1/2 and cos(alpha+bita)=1/2, where alpha and bita are positive acute angles then what is the value of alpha and bita
  4. trig

    FInd the exact value pf the 6 trig function of alpha Given: point (-2,-6) on the terminal side of the angle in standard position sin alpha cos alpha tan alpha sec alpha csc alpha cot alpha
  5. math

    This is the problem given: The side of a hill faces due south and is inclined to the horizontal at an angle alpha. A straight railway upon it is inclined at an angle beta to the horizontal. If the bearing of the railway is gamma east …
  6. mat- foundation of mechanic

    a particle is projected from a point 0 with an initial speed of 30m/s to pass through a point which is 40m from 0 horizontally and 10m above 0. show that there are two angles of projection for which this is possible. if these angles …
  7. Calculus

    The question will first read in English followed by a reading in French. *************************************** If alpha + 2 beta = pi/4 AND tan beta = 1/3. What would tan alpha mesure?
  8. physics

    Two radar stations A and B, are separated by horizontal distance of (a=500 metres), they both track the position of a plane C by recording angles (alpha), and (beta) at 1 second intervals. time (sec) 9 10 11 the angle A(alpha) 54.80 …
  9. trig

    evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(beta-alpha) …
  10. algebra

    if sin alpha is 0.28° where 0° is less than or equal to alpha less than or equal to 90°, evaluate cos alpha, tan alpha, sec alpha, cosec alpha and cot alpha. please help, it's urgent.

More Similar Questions