Pleease Help, trig question?

Question

It says to solve each of the following from (0, 2pi)

1. sinx= -4/5
2. cosx=2/3
3. secx=3

x= angle theta

Answer 1

1). sin(x) = -4/5

sin(x) = -0.8

Apply 'Sin^-1' each side.

Sin^-1[sin(x)] = Sin^-1(-0.8)

x = Sin^-1(-0.8)

Trigonometric table in sin233°.2' = -0.8

x = Sin^-1(sin233°.2')

x = 233°.2'.

 

2). cos(x) = 2/3

cos(x) = 0.666

Apply 'cos^-1' each side.

cos^-1[cos(x)] = cos^-1[0.666]

x = cos^-1[0.666]

Trigonometric table in cos48° = 0.66

x = cos^-1[cos48°]

x = 48°

 

3). secx = 3

Reciprocal identities: secθ = 1/cosθ

1/cos(x) = 3/1

Cross multiplication

cos(x) = 1/3

cos(x) = 0.333

Apply 'cos^-1' each side.

cos^-1[cos(x)] = cos^-1[0.333]

x = cos^-1[0.333]

Trigonometric table in cos70°.5' = 0.333

x = cos^-1[cos70°.5']

x = 70°.5'.