Trigonometry 1 find the remaining trig ratios secphi 35 pi2

Trigonometry:

1. find the remaining trig ratios

sec(phi) = -3.5, pi/2 < phi < pi

sin-

cos-

tan-

csc-

cot-

2. If sin(x) = 1/3 and sec(y) = 13/12, where x and y lie between 0 and /2, evaluate the expression using trigonometric identities. (Enter an exact answer.)

sin(2y)=

i got 2(3/13)(12/13) but I am doing something wrong...

3. Find all values of x in the interval [0, 2] that satisfy the equation. (Enter your answers as a comma-separated list.)

10 cos(x) 5 = 0

x=

the more work you show, the more I can learn. thanks in advance

Solution

1) sec(phi) = -3.5, pi/2 < phi < pi

cos(phi) = -1/3.5 = -0.28

sin(phi) = sqrt( 1- cos^2(phi) ) =0.96

tan(phi) = sinphi/cosphi = -3.43

csc(phi) = 1/sin(phi) =1.042

cot(phi) =1/tanphi = -0.29

2) There is something wrong it seems we have sinx and siny and you wnat only

sin(2y) , we would not use sinx

sin2y = 2sinycosy

secy = 13/12 ; cosy = 12/13

siny = 5/13

So, siin2y = 2*12/13*5/13 =120/169

3) 10cosx -5 =0

interval [0, 2]

cosx = 5/10

cosx = 0.5

x = cos^-1(0.5) = pi/3 , 2pi-pi/3 = pi/3, 5pi/3