Find the remaining trigonometric ratios

[Math_Junkie]

Given: sec(theta) = -1.5, pi/2 < theta < pi
Find the remaining trigonometric ratios: sin(theta), cos(theta), tan(theta), csc(theta), cot(theta)

Since -1.5 is not part of the special angles, I'm unsure as to how to approach this question.

Any help/suggestions will be greatly appreciated!

 

[Loren]

Given: sec(theta) = -1.5, pi/2 < theta < pi
Find the remaining trigonometric ratios: sin(theta), cos(theta), tan(theta), csc(theta), cot(theta)

Since -1.5 is not part of the special angles, I'm unsure as to how to approach this question.

Any help/suggestions will be greatly appreciated!

If it said Given: csc x = 2.5, would you realize that is saying csc x = 5/2? Then you could draw a right triangle and label the two appropriates sides as 5 and 2. You could then use the Pythagorean Thm. to find the length of the hypotenuse. Then you would read off the values of the remaining functions directly from the drawing.

 

[Math_Junkie]

I tried your advice and got:

csc(theta) = 3/sqrt(5)
sec(theta) = -3/2
cot(theta) = -2/sqrt(5)
sin(theta) = sqrt(5)/3
cos(theta) = -2/3
tan(theta) = -sqrt(5)/2

Is this correct?

 

[Mrspi]

I tried your advice and got:

csc(theta) = 3/sqrt(5)
sec(theta) = -3/2
cot(theta) = -2/sqrt(5)
sin(theta) = sqrt(5)/3
cos(theta) = -2/3
tan(theta) = -sqrt(5)/2

Is this correct?

Looks good!