Using a Unit Circle, what is the exact value of tan space left parenthesis 45 degree right parenthesis?

Answer 1

tangent of 45 degrees = 1

tangent is the opposite side over the adjacent side. That's for a unit circle: (1/2)sqr2/(1/2)sqr2 = 1 exactly

tan45 = sin45/cos45 = (1/2)sqr2/(1/2)sqr2 = 1

Answer 2

Hey, I hope you’re doing well!

For this problem, we can start with the definition of tangent (sine over cosine).

tan = sin/cos

Then, we look on the unit circle and see what point corresponds to 45 degrees. We see (√2/2, √2/2). (The square roots are just over the numerators.) Now, we know that the unit circle points follow the format of (cos, sin), so if we want the tangent (sine/cosine), we get:

tan = sin/cos

tan = (√2/2)/(√2/2)

tan = 1 ← Since dividing a number by itself is 1

So, 1 is our answer.

I hope that helped! Take care!