Six trigonometric function???

Question

A. Give the six trigonometric function values of the given real numbers.

1. pi/3

2.5pi/3

3.-3pi

4.(-3pi)/2

5.-7pi/4

6.19pi/3

*the six trigonometric functions are sin,cos,tan,csc,sec, and cot.

hope you can help me guyz!

Answer 1

use the scientific calculator function for each:

for sin,  use   sin^-1  to get the angle corresponding to each.

for tan, use tan ^-1....  cos^-1 for cos angles

for ex:   pi/3  = 60 degree...   (make sure your calculator is in degree mode)   and then type (usually 2nd func. key) and sin to get your value...

same for the other functions,

good luck

Answer 2

1.  sin(pi/3) = sqrt(3)/2

     cos(pi/3) = sin (pi/2 - pi/3) = sin(pi/6) = 1/2

     tan(pi/3) = sqrt(3)

     csc(pi/3) = 1/sin(pi/3) = 2/sqrt(3)

     sec(pi/3) = 1/cos(pi/3) = 2

     cot(pi/3) = 1/tan(pi/3) = 1/sqrt(3)

Answer 3

convert the radian into degrees

1) pi/ 3 x  180/pi = 180/3 =  60 degrees

sin 60 =  sqrt 3/2

csc 60 = 1/sin 60 = 1/ sqrt 3/2 = 2/sqrt 3

cos 60 = sqrt 1 - sin^2 60 = sqrt 1 - (sqrt 3/2)^2 =  sqrt 1 - 3/4 =

cos 60 = sqrt 4/4 - 3/4 = sqrt 1/4 =  1/2

sec 60 = 1/cos 60 =  2/1 = 2

tan 60 = sqrt sec^2 60 - 1 = sqrt 2^2 -1 = sqrt 4-1 = sqrt 3

cot 60 = 1/tan 60 = 1/ sqrt 3

DO the same to the rest. Convert frist radians itno degrees by  180/pi.

And then use the identity.

Answer 4

1) pi/ 3 x 180/pi = 180/3 = 60 degrees

sin 60 = sqrt 3/2

csc 60 = 1/sin 60 = sqrt 3 / 2

cos 60 = sqrt 1 - sin^2 60 = sqrt 1 - (sqrt 3/2)^2 = sqrt 1 - 3/4 =

cos 60 = sqrt 4/4 - 3/4 = sqrt 1/4 = 1/2

sec 60 = 1/cos 60 = 2/1 = 2

tan 60 = sqrt sec^2 60 - 1 = sqrt 2^2 -1 = sqrt 4-1 = sqrt 3

cot 60 = 1/tan 60 = sqrt 3/3

2.  5 pi/ 3 = 5*180/3 = 300 degrees

sin 300 = -sqrt 3/2

csc 300 = 1/sin 300 = -2/sqrt 3

cos 300 =  1/2

sec 300 = 1/cos 300 = 2/1 = 2

tan 300  = -sqrt 3

cot 300 = 1/tan 300 = -sqrt 3/3

3. - 3 pi = - 3 * 180 = -540

sin -540 = 0

csc -540 = 1/sin -540 = undefined

cos -540 =  -1

sec -540 = 1/cos -540 = -1

tan -540  = 0

cot -540 = 1/tan -540 = undefined

4. - 3 pi / 2 = - 3 * 180 / 2 = -270

sin -270 = 1

csc -270 = 1/sin -270 = 1

cos -270 =  0

sec -270 = 1/cos -270 = undefined

tan -270  = undefined

cot -270 = 1/tan -270 = 0

5.   - 7 pi / 4 = - 7 * 180 / 4 = -315

sin -315 = sqrt 2 / 2

csc -315 = 1/sin -315 = sqrt 2

cos -315 =  sqrt 2 / 2

sec -315 = sqrt 2

tan -315 = 1

cot -315 = 1/tan -315 = 1

6.    19 pi / 3 = 19 * 180 / 3 = 1140

sin 1140 = sqrt 3/2

csc 1140 = 1/sin 1140 = 2 sqrt 3 / 2

cos 1140 = 1/2

sec 1140 = 1/cos 1140  = 2

tan 1140  = sqrt 3

cot 1140 = 1/tan 1140 = sqrt 3/3