Question

Find the exact real value of arccos(-sqrt(2)/2).

Answer 1

\[\arccos(-\sqrt{2}, 2)\]

Answer 2

@RadEn

Answer 3

Do you have a calculator?

Answer 4

Yes! But when I put it in my calculator, I get 135, and my choices are pi/4, 3pi/4, 7pi/4, and -pi/4... :c

Answer 5

You need to convert from deg to radians.

Answer 6

Ohhh. That makes more sense! Thanks!

Answer 7

What did you get? Also on your calculator you may have a deg button that allows you to switch to radians.

Answer 8

I found it, it was under mode. And I got 3pi/4. :)

Answer 9

Do you know how to do this one? I think I'm supposed to do it without a calculator! :/ --> Find the exact value of cos(arcsin()). For full credit, explain your reasoning.

Answer 10

\[\cos(\arcsin(1/4))\]

Answer 11

Huh?

Answer 12

What can you tell me about the lengths of sides in a right angled triangle?

Answer 13

BG: Indivicivet is on the right track in coming up with a diagram representing the angle arcsin(1/4). Since the sine is defined as "opposite side divided by hypotenuse," we can safely assume that the opposite side is 1 and the hypotenuse is 4.

Using the Pyth. Thm., find the length of the adjacent side.

Now you'll know all three sides of the triangle of which arcsin (1/4) is a part.

cos (angle_ = adj/hyp, so here just plug in the values of adj and hyp and you're done. You'll have the cosine of arcsin (1/4).

Answer 14

Once you've done this a few times, I think you'll find that the work involved is a lot easier than it looks. Keep in mind that arcsin (1/4) is an ANGLE, and from it you can tell that the opp side of this angle is 1 and the hyp is 4. That means the adj side is Sqrt(4^2-1^2).

Answer 15

BG: Don't take it personally, but I have to get off the computer to do some errands. I'll look forward to working with you again soon.

Answer 16

Okay.. :c I think I can get it from your help! Thanks again!