Math Specific Triangles, Grade 11 Trigonometry

  • Determine the values of sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ at (-3, -4) on the terminal arm of an angle θ in standard position.
  • If cosθ = 2/3 and 270° < θ 360° , then determine the exact value of (1/cotθ).
  • Find the exact value of the following, show all work:
  • sin2(75°) sin 45° cos230° (Hint: sin2θ = (sinθ)2 )
  • tan(135°) + sin(30°)cot(120°)
  • Evaluate the following, give exact value when possible:
  • sec(225°)
  • sin(-15°)
  • sin(75°)
  • Given:csc θ = −(17/15), where 270° ≤ θ ≤ 360° and cot β = −(3/4) where 90° ≤ β ≤ 180°.Find the exact value of sin(θ + β). Show all the work.
  • Expert Answers

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    I have answered what I am permitted to: q1)

    The triangle will appear in Quad III as both x and y are negative

    (-3;-4).

    The angle `theta`  sits between the x-axis and the arm. First calculate the hypoteneuse: `(-3) ^2 + (-4)^2` `= h^2`

    Therefore: h = `sqrt(25)`  = 5

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    I have answered what I am permitted to: q1)

    The triangle will appear in Quad III as both x and y are negative

    (-3;-4).

    The angle `theta`  sits between the x-axis and the arm. First calculate the hypoteneuse: `(-3) ^2 + (-4)^2` `= h^2`

    Therefore: h = `sqrt(25)`  = 5

    Thus: `sin theta = -4 /5`   that is opposite / hypoteneuse

    Now do `cos theta`  and `tan theta` the same way .

    For cosec sec and cot remember to invert your equation as

    `cosec theta = 1/ sin theta`  `sec theta = 1/ cos theta`  and `cot theta = 1/ tan theta`

    Thus final answer: `sin theta`  = -4 / 5

     

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