Find the value of tan theda if sin theda = -3/8 and sec theda <0?

Question

i think i know what the answer is..just double checking

Answer 1

I take it that by &quot;theda&quot; you mean the Greek letter &quot;theta&quot;?

If the sine is negative, then that means θ is in the 3rd or 4th quadrant.  If the secant is negative there too, then it has to be the 3rd quadrant.  The tangent is positive there.

If you have a triangle where the opposite side is 3 and the hypotenuse is 8, then you can use the Pythagorean theorem to find the adjacent side, and the fact that tan(θ) = opposite / adjacent to get the value.

Answer 2

sec t is negative therefore cos t is negative

And sin t is also negative therefore pi &lt;= t &lt;= 3/2 pi.

sin t = -38

Let t = pi + x then sin t = sin pi cos x + cos pi sin x = 0 - sin x

sin x = 3/8

cos x = sqrt(1- sin^2 x) = sqrt( 1 - 9/64) = sqrt (55/64) = (sqrt 55)/8

tan x = 3/sqrt(55)

tan has period pi so tan t = tan (pi + x) = tan x = 3/sqrt(55)