Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

120,929 users

find the exact values of the following:

0 votes

1. sec30° 
2. cos75° 
3. cot 2π/3 
4. cos π/8

asked May 4, 2014 in TRIGONOMETRY by anonymous

1 Answer

0 votes

1). sec 300 .

  • π/6 is in quadrant 1 and there is no need for either coterminal or reference angles.

  • In quadrant 1 the secant is positive.

  • So, sec (π/6) is evalueated directly as follows.

           sec (π/6) = 2/√3.

2). cos 750 .

  • 750 is in quadrant 1.in quadrant 1 the cosin is positive.

          hence

  • cos (750) = cos (450 + 300)

                         = cos 45 cos 30 - sin 45 sin 30                                   ( cos (A + B) = cos A cos B - sin A sin B)

                         = (1/√2)(√3/2) - (1/√2)(1/2)

                         = (√3 - 1)/2√2.

3). cot (2π/3).

  • 2π/3 is in second quadrant.in second quadrant the tangent and cotangent are negative.

           hence

  • cot (2π/3) = cot (π - 2π/3) = - cot (π/3) = - 1/√3.

4). cos (π/8).

  • π/8 is in quadrant 1 and there is no need for either coterminal or reference angles.
  • In quadrant 1 the cosin is positive.

            hence

  • cos(2(π/8)) = 2 cos^2(π/8) - 1                                           (cos (2x) = 2cos^2 (x) - 1)

           ⇒ cos (π/8) = √{ [ cos(2(π/8)) + 1 ]/2 }

                             = √{ [ cos(π/4) + 1 ]/2 }

                             = √{ [√2/2 + 1 ]/2 }

                             = √( 2+√2)/2

                             = 0.9238.

answered May 6, 2014 by lilly Expert

Related questions

...