mathematics

posted by .

find the maximum value of √3 cosθ-sinθ.???

  • mathematics -

    You get a maximum when the derivative is zero.

    -ã3 sin ƒÆ -cos ƒÆ = 0
    tan ƒÆ = -1/ã3

    Į = -30 degrees

    ã3 cosƒÆ-sinƒÆ = 3/2 + 1/2 = 2

    check: If theta = -29 degrees,
    ã3 cosƒÆ-sinƒÆ = 1.5149 + 0.4848 = 1.9997
    If theta = -31 degrees,
    ã3 cosƒÆ-sinƒÆ = 1.4847 + 0.5150 = 1.9997
    So it looks like the maximum is 2.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Calculus

    The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a …
  2. math

    if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
  3. trigonometry

    if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
  4. Pre-Calculus

    If θ represents an angle such that sin2θ = tanθ - cos2θ, then sin θ - cosθ = A. -√2 B. 0 C. 1 D. 2√2 What equation can I use to solve this problem?
  5. math trigono

    1. If tanθ = –√3 , what is the value of cot ?
  6. Quantum Physics

    We have a qubit in the state |ψ>= √3/2 |0>+ 1/2 |1>, which we want to measure in the {Cos θ |0> + Sin θ |1>, Sin θ |0> - Cos θ |1>} basis. In order for the two possible outcomes to …
  7. Physics

    We have a qubit in the state |ψ>= √3/2 |0>+ 1/2 |1>, which we want to measure in the {Cos θ |0> + Sin θ |1>, Sin θ |0> - Cos θ |1>} basis. In order for the two possible outcomes to …
  8. trig

    An object Is propelled upward at an angle θ, 45° < θ<90°, to the horizontal with an initial velocity of (Vo) feet per second from the base of a plane that makes an angle of 45° with the horizontal. If air resistance …
  9. Trigonometry

    There are four complex fourth roots to the number 4−4√3i. These can be expressed in polar form as z1=r1(cosθ1+isinθ1) z2=r2(cosθ2+isinθ2) z3=r3(cosθ3+isinθ3) z4=r4(cosθ4+isinθ4), …
  10. Math (Trigonometry)

    θ is an acute angle such that tan(θ)=1/4. What is the value of 17√17*(sinθ+cosθ)?

More Similar Questions