Finding values of trig functions

[jtw2e2]

Find the values of the trig functions of t if sect=2 and sint<0.

Here are my answers, all work is shown below:

sect = 2
cost = 1/2
sint = -?(3)/2
csct= (2/?(3))
tant= ?(3)
cott= 1/?(3)

Solving for cost
sect= (1/cost) Therefore:
2 = 1/cost=1/2

Solving for sint
From the Pythagorean Identities we have:
sin^2t + cos^2t = 1
sin^2t + (1/2)^2 = 1
sin^2t = 1 - 1/4
sin^2t = 3/4
sint = ±?(3/4)
sint = -?(3)/2 (Negative because instructions say sint<0 ????

Solving for csct
csct=(1/sint)
csct= (2/?(3))

Solving for tant
tant=(sint/cost)
tant= [?(3)/2]/[1/2]
tant= ?(3)

Solving for cott
cott= 1/tant
cott=1/?(3)

Would someone tell me if I am correct?

 

[Deleted member 4993]

Find the values of the trig functions of t if sect=2 and sint<0.

Here are my answers, all work is shown below:

sect = 2
cost = 1/2
sint = -?(3)/2
csct= -(2/?(3))<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
tant= -?(3)<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
cott= -1/?(3)<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Solving for cost
sect= (1/cost) Therefore:
2 = 1/cost=1/2

Solving for sint
From the Pythagorean Identities we have:
sin^2t + cos^2t = 1
sin^2t + (1/2)^2 = 1
sin^2t = 1 - 1/4
sin^2t = 3/4
sint = ±?(3/4)
sint = -?(3)/2 (Negative because instructions say sint<0 ????

Solving for csct
csct=(1/sint)
csct= -(2/?(3)) <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Solving for tant
tant=(sint/cost)
tant= [?(3)/2]/[1/2]
tant= -?(3)<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Solving for cott
cott= 1/tant
cott= -1/?(3)<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Would someone tell me if I am correct?

 

[jtw2e2]

Subhotosh Khan,

Thanks a lot for pointing those out. After a little more experience I'm beginning to become familiar with where the different Trig functions are positive and negative and why that is so.