Question

Use a special triangle on the unit circle to determine the value of tan π/ 4 .

A) 1

B) 1/ 2

C)√ 2/ 2

D)√ 2/ 3

Answer 1

Remember for your previous question

\( 2\pi = 360^o\)

so can you tell me what \(\dfrac{\pi}{4}\) would be in degrees?

Answer 2

45

Answer 3

Exactly!! Do you know the side ratios for a 45-45-90 triangle?

Answer 4

No

Answer 5

So when you have the same angles, that means that those side lengths are the same

So for example, if the side length of the side opposite angle 45 was 1
then the other side opposite the angle 45 is going to be 1

and since it's a right angle triangle, can you use Pythagorean theorem to calculate what the hypotenuse would be?

Answer 6

Would it be 90?

Answer 7

No no

Remember Pythagorean theorem

a^2 + b^2 = c^2

where a and b is the legs of the triangle
(which is 1 in this case)

and c is the hypotenuse

Answer 8

-63.6? Im not sure

Answer 9

Well no

a^2 + b^2 = c^2

c is the hypotenuse which is the longest side of the triangle
the side opposite the 90 degrees

and the two legs of the triangle are 1

1^2 + 1^2 = c^2

can you solve for c?

Answer 10

Im gonna be honest with you I honestly dont know

Answer 11

what is 1^2

Answer 12

1

Answer 13

Good!

So what is 1 + 1 = ?

Answer 14

2

Answer 15

So now we went from

1^2 + 1^2 = c^2

1 + 1 = c^2

and then

2 = c^2

so to find c, you just have to take the square root on both sides

so c = sqrt(2)

does that make sense?

Answer 16

So do you know that

tan = opposite/adjacent

Answer 17

I got 1

Answer 18

You said that pi/4 (which is in radians) is the same thing as 45 degrees

so tan 45

Look at the triangle
What is the side opposite the angle 45 and what is the side adjacent to it?

And remember, the hypotenuse is different

Answer 19

Thank you!

Answer 20

You're welcome!