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Trigonometry Test - 4

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Trigonometry Test - 4
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Weekly Quiz Competition
  • Question 1
    1 / -0
    In a right PQR, right-angled at Q, PR – PQ = 2 units and QR = 4 units. What is the measure of PR?
  • Question 2
    1 / -0

    The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

    Solution

     

  • Question 3
    1 / -0
    If cos( + ) = 0, then sin( - ) can be reduced to
  • Question 4
    1 / -0

    There exists a triangle ABC satisfying the conditions

    Solution

     

     

  • Question 5
    1 / -0
    Which of the following expressions is rational?
  • Question 6
    1 / -0

    If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

    Solution

    Let the sides of the triangle be a=13,b=7 and c=8.

    Since a  is the longest side the greatest angle is A.

    Using Cosine rule, we have  

    osA=b2+c2−a2 / 2bc=49+64−169/112=−12But we have cos(2π/3)=cos(π−π/3)=−cos(π/3)=−1/2

    ∴A=2π3

  • Question 7
    1 / -0
    The value of the expression  is
  • Question 8
    1 / -0
    The value of (tan 1° tan 2° tan 3° ... tan 89°) is
  • Question 9
    1 / -0
    What is the value of sin. cos[tan + cot]?
  • Question 10
    1 / -0
    If cos 9 = sin and 9 < 90°, then the value of tan 5 is
  • Question 11
    1 / -0
    If tan + sec = ; 0 <  <, then  is equal to
  • Question 12
    1 / -0
    Find the value of the following expression:

    [cosec (75° + ) – sec (15° – ) – tan (55° + ) + cot (35° – )]
  • Question 13
    1 / -0
    If  is right-angled at C, then the value of cos (A + B) is
  • Question 14
    1 / -0
    If sin A + sin 2A = 1, then the value of the expression (cos2A + cos4A) is
  • Question 15
    1 / -0
    If sin A = 1/2, then the value of cot A is
  • Question 16
    1 / -0
    Find the value of cos 30o . cos 60o . ------- cos 90o . cos 220o.
  • Question 17
    1 / -0
    If sin = cos , then  is equal to
  • Question 18
    1 / -0
    cot + tan equals
  • Question 19
    1 / -0

    In a ΔABC, (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to

    Solution

    (b+c)cosA+(c+a)cosB+(a+b)cosC=b.cosA+c.cosA+c.cosB+a.cosB+a.cosC+b.cosC=(b.cosC+c.cosB)+(a.cosC+c.cosA)+(b.cosA+a.cosB)=a+b+c [usingprojectionrule]

  • Question 20
    1 / -0
    If 4 tan  = 3, then  is equal to
  • Question 21
    1 / -0
    The value of sin (45° + ) – cos (45° – ) is equal to
  • Question 22
    1 / -0
    If sin = 1/2 and cos = 1/2, then the value of  is
  • Question 23
    1 / -0
    If sin – cos = 0, then what is the value of (sin4 + cos4)? [Given ()]
  • Question 24
    1 / -0
    The maximum value of sin x is
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