Question

Find the value of sec theta for the angle shown. The point is (7,6)

Answer 1

Hello again ms Krissie :)

So we're in the first quadrant.

Answer 2

Use your Pythagorean Theorem.
What is the length of the hypotenuse?

Answer 3

9?

Answer 4

\[\Large\rm a^2+b^2=c^2\]\[\Large\rm 7^2+6^2=c^2\]Hmm I don't think that's going to work out nicely to 9 :o

Answer 5

\[\Large\rm 85=c^2\]Then square root to get your hypotenuse, yah?

Answer 6

thats what I did, i got c^2=85 and the sqrt of it is about 9

Answer 7

Yah a little over 9 :)
They'll probably want you to keep the answer exact though.
\[\Large\rm c=\sqrt{85}\]

Answer 8

So to find secant, relate it back to cosine first.\[\Large\rm \sec \theta=\frac{1}{\cos \theta}\]

Answer 9

secant is the flip of cosine.
Recall that:\[\Large\rm \cos \theta=\frac{adjacent}{hypotenuse}\]

Answer 10

So our secant will be the flip of that,\[\Large\rm \sec \theta=\frac{hypotenuse}{adjacent}\]

Answer 11

I'm so confused.. what do i plug in and where

Answer 12

\[\Large\rm \sec \theta=\frac{hypotenuse}{adjacent}\]We labeled the sides.
Look back at the picture :o

Answer 13

\[\Large\rm \sec \theta=\frac{hypotenuse}{7}\]

Answer 14

Hypotenuse was the thing we figured out using our Pythagorean Theorem, yes?

Answer 15

yes, so it's 9/7 right?

Answer 16

so let's pick where @zepdrix left
\(\huge {sec\theta=\frac{1}{cos\theta}} \Longrightarrow cos\theta=\frac{1}{sec\theta}=\frac{7}{\sqrt{85}}\)

Answer 17

to get sec just flip that fraction

Answer 18

@KrissieG123 the hypothenuse is not 9 is bigger than 9
just keep it \(\sqrt{85}\)

Answer 19

oh okay so wait, is that the answer? or s there another step? The choices are:
A. sec=(7sqrt85)/85
B. sec=6/7
C. sec=7/6
D. sec=sqrt 85/7
It would be D right?

Answer 20

yes! one you flip to get sectheta
you would get the answer D

Answer 21

Okay, thank you so much!!

Answer 22

np!