Question

Find the exact value of each of the remaining trigonometric functions of theta.

Rationalize denominators when applicable.
sin theta=
`\sqrt{(3)/(7) }` given that theta is in quadrant I.
cos theta=
csc theta=
sec theta=
tan theta=
cot theta=

Answer 1

See answers below

Explanation:

Given that sin theta = √3/√7

Opposite =√3

Hypotenuse = √7

Get the adjacent

Adj² = (√7)²-(√3)²

Adj² = 7-3

Adj² = 4

Adj = √4

Adj = 2

Cos theta = adj/hyp = 2/√7

csc theta= 1/sin theta = 1/(√3/√7) =

√7/√3

sec theta= 1/costheta = 1/(2/√7) = √7/2

tan theta= opp./adj = √3/2

cot theta =1/tan theta = 1/(√3/2) = 2/√3

= 2√3/3