Question

(Trigonometry) I'm not understanding the steps to solving this problem, may someone please help? P(-5,5) is a point on the terminal side of theta in standard position. What is the exact value of secant theta?

Answer 1

I got 7 using the pythagorean therom.

Answer 2

Consider the definition of secent. Secent is inverse cosine, and cosine is
\[\frac{\text{adjacent}}{\text{hypotenuse}}\]
Which means that secent will be
\[\frac{\text{hypotenuse}}{\text{adjacent}}\]

Answer 3

Okay, so it'd be 7/5, yes?

Answer 4

Good work =)

Answer 5

Clearly the secant (reciprocal of the cosine) will be negative in quadrant 2.
Calculate the hypotenuse using the fact that the hypotenuse of a 45-45-90 triangle if leg multiplied by sqrt2

Answer 6

Oh, wait. One minor issue. -5 is the adjacent side.

Answer 7

Right (: Because of the coordinates

Answer 8

Yes. Well done.

Answer 9

That cannot be correct. The hypotenuse is 5sqrt2 and so the secant is -5sqrt2/5or -sqrt2

Answer 10

I know, it's just easier for me to start off with the number than it is with the square roots.

Answer 11

Ah, yes. Mertsj is correct. You made some mistake in calculating the hypotenuse.

Answer 12

Well, you can make up any answer you want but it will not be correct.

Answer 13

Ah, alrighty. How do I work with the 5 square root 2?

Answer 14

Just leave it as it is.

Answer 15

still dd not get ? o.0

Answer 16

\[\sec x=\frac{hypotenuse}{side adjacent}=\frac{5\sqrt{2}}{-5}=-\sqrt{2}\]

Answer 17

Oh my gosh, THANK YOU :D That makes sense to me Lol.

Answer 18

yw

Answer 19

Nora, do you understand how to get the hypotenuse?

Answer 20

That is the only thing I am still confused on :/

Answer 21

Do you know the :Pythagorean Theorem?

Answer 22

\[5^2+5^2=hypotenuse^2\]

Answer 23

Yes, \[a ^{2} + b ^{2} = c ^{2}\]

Answer 24

You were right that we need to use the pythagorean theorem. Set up an equation using
a^2 + b^2 = c^2
and make sure that you use the hypotenuse for c.

Answer 25

Okay, 5^2 + (-5)^2 = c^2
25 + 25 = c^2
50 = c^2

Answer 26

Good. Keep going. Solve for c.

Answer 27

\[\sqrt{50}\] = 7.07

Answer 28

The problem asked for the EXACT value so you have to keep it in simplified radical form

Answer 29

Well. Yes, sqrt(50)
but this is where it's better not to plug it into your calculator and round it like you did.

Answer 30

\[\sqrt{50}=\sqrt{25(2)}=5\sqrt{2}\]