Question

Find the exact value of the remaining trigonometric functions of theta: sec(theta)=4 , cot>0.

Answer 1

ok, first of all \[\sec \theta = 1/\cos \theta \]

Answer 2

Since sec (theta) = 4 we can say 1/cos (theta) = 4

Answer 3

true

Answer 4

\[1/\cos \theta = 4\]
multiply both sides by cos (theta)

\[4 \cos \theta = 1 \]

Answer 5

cos = 1/4 then? which makes x=1 and radius of the unit circle 4?

Answer 6

right

Answer 7

ok how do I find sin(theta) from there?

Answer 8

To get sin (theta) you need to find y. Use the pythagorean theorem a^2 + b^2 = c^2, (a=x, b=y, and c=r) and since both the sec and cot are positive, the angle is in the first quadrant, so y is also going to be positive.

Answer 9

1+ y^2 = 16
y^2 = 15
\[y = \sqrt{15}\]

Answer 10

i got root(15) from that for y. so sin would be root(15) or since sine is y over radius would it be root(15)/4?

Answer 11

since sin is y/r you need \[\sqrt{15}/4\]

Answer 12

Alright I think I have it from here. thanks so much for your help.

Answer 13

yup.