Question

find sec theta if tan theta =7/24 and cos theta < 0.

Answer 1

do you know which quadrant has tan as positive and cos negative..?

Answer 2

quadrant 3

Answer 3

great so drawing a diagram for quadrant 3



can you now find c, the hypotenuse using pythagoras?

Answer 4

he said do not draw a triangle to use the identities I think

Answer 5

c=sqrt(a^2+b^2)

Answer 6

ok then so you need to know

\[\sin^2(\theta) + \cos^1(\theta) = 1\]

dividing every term by cos^2 gives

\[\tan^2(\theta) + 1 = \sec^2(\theta)\]

so substituting

\[(\frac{7}{24})^2 + 1 = \sec^2(\theta)\]

so evaluate this and then take the square root.

then use the negative value.

Answer 7

hope it helps

Answer 8

thanks so much I just found where I wrote it all down in my notes !!!