59.7k views
4 votes
What is cos theta of tan theta= 8/5?

User Zango
by
8.3k points

2 Answers

5 votes
The tangent ratio is the side opposite the reference angle over the side adjacent the reference angle. If you set up a right triangle in the first quadrant where both x and y are positive, the side opposite the reference angle is 8 and the stationary part of the angle is on the x axis as 5. We are now lacking the hypotenuse measure of this right triangle. Find it with Pythagorean's Theorem. c^2 - 8^2 + 5^2. c^2 = 64 + 25, so the length of the hypotenuse is sqrt 89. The cosine ratio is the side adjacent over the hypotenuse, so the cosine of that same angle is 5/sqrt89.
2 votes
I'd suggest you write:

":What is cos theta IF tan theta= 8/5?

tan theta = opp / adj = 8 / 5, so we know that opp = 8 and adj = 5. Then the length of the hypotenuse is sqrt(8^2+5^2) = 9.43.

Thus, the cosine of theta / cosine of this angle is

adj 5
----- = ---------- , or about 0.53.
hyp 9.43
User Phil Gyford
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.