Find the exact value of each of the other five trigonometric

Find the exact value of each of the other five trigonometric functions for the angle x : cos x = -3/5 and x is in quadrant IV. Verify whether the point P lies on the unit circle Find the exact value of each of the six trigonometric functions if the terminal side of angle x contains the point P = (- 6.3) Find the velocity of a point on the rim of the wheel if r = 2 feet and Find the angular velocity if r = 25m and V - 120m/min . Find the angular velocity of a wheel turning through K radians in 30 seconds switch the angle -140

Solution

10) given cosx =-3/5

but it is wrong

cos x >0 in Q_IV

if it is cosx =3/5

cosx =adjacent side/hypotenuse= 3/5

hypotenuse²=opposite side²+adjacent side²

5²=opposite side²+3²

opposite side²=25-9

opposite side²=16

opposite side=4

sin x <0 in Q_IV

sinx =opposite side/hypotenuse= -4/5

tanx =sinx/cosx=-4/3

cotx=1/tanx =-3/4

cscx =1/sinx=-5/4

secx=1/cosx=5/3

11) radius of unit circle is 1

so for any point in unit circle distance between origin(0,0) and point(-3 /2 ,1/4) should be less than 1

distance between origin(0,0) and point(-3 /2 ,1/4) =[(-3 /2 -0)²+(1/4)²]

distance between origin(0,0) and point(-3 /2 ,1/4) =[(3 /4)+(1/16)]

distance between origin(0,0) and point(-3 /2 ,1/4) =[13/16]

distance between origin(0,0) and point(-3 /2 ,1/4) <1

so point is inside unit circle