Question

Find the values of the trigonometric functions of t from the given information.
sec(t) = 6, sin(t) < 0
need sin(t, cos(t), csc(t), tan(t), cot(t)

Answer 1

\[\sec(t) = 1/\cos(t)\] so:\[1/\cos(t) = 6 \]\[\cos(t) = 1/6\]

then:
\[c^2 = x^2 + y^2\]

\[y^2 = c^2 - x^2 = (36)-1 = \sqrt{35}\]

so:
\[\sin(t) = \sqrt{35}\]
\[\csc(t) = 1/\sin(t) = 1/\sqrt{35}\]
\[\tan(t) = \sin(t)/\cos(t) =6\sqrt{35}\]
\[\cot(t) = 1/\tan(t) = 1/6\sqrt{35}\]

^_^

Answer 2

wait the hyp =36 so :

sin(t) = sqrt(35)/36
csc(t) = 36/sqrt(35)
tan(t) = sqrt(35)/6
cot(t) = 6/sqrt(35)


Sorry for the mess ^^" .