anonymous one year ago The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

1. anonymous

2. anonymous

@pooja195

3. anonymous

@phi

4. Zale101

|dw:1438125246483:dw|

5. Zale101

|dw:1438125391747:dw|

6. anonymous

|dw:1438125791505:dw|

7. Zale101

You first, find all the sides, and use trig identities to determine what cosine, sine, and tangent are. $$cos(\theta)=\Large \frac{Adjacent}{Hypotenuse}$$ $$sin(\theta)=\Large \frac{Opposite}{Hypotenuse}$$ $$tan(\theta)=\Large \frac{Opposite}{adjacent }$$

8. Zale101

|dw:1438125668700:dw|

9. anonymous

the degree

10. Zale101

I used the Pythagorean theorem to find r, since we already have x and y given (2,3)

11. Zale101

how did you find the degree?

12. anonymous

using the unit circle

13. Zale101

The unit circle shifts 1 unit across and 1 unit upward and downward. There's no point (2,3) on the unit circle.

14. Zale101

However, there's degrees and radians which applies to all circle.

15. Zale101

circles*

16. Zale101

You are given a point. You find all the sides of the triangle. Use trig identities and then inverse to solve for the angle. Your goal is to find angle theta and that is the steps to find it.

17. Zale101

I'm still confused on how you got theta straight from looking at the unit circle.

18. anonymous

because i know in the unit circle pi/4 is in the middle and that is 45 degrees and because point (2,3) looks like its in the middle i had just assume that it would be 45 degrees

19. Zale101

Although the correct degree is closer to 45, 45 degrees is incorrect. Therefore, your assumption is wrong. If the point was (2,2), then theta is 45 degrees. We don't assume the answers with trig, we do math just like how we do math to solve for x in algebra but slightly different. Math is math. We do math to solve for math problems.

20. Zale101

Here are the steps to your problem when finding the terminal side of angle θ by a given point Step 1: Label the given point on the graph Step 2: Draw a right triangle and label the sides. X, y, and r (like i did above) Step 3: Label the adjacent and opposite sides. (x, y) x is the adjacent, y is the opposite sides Step 4: Use the Pythagorean theorem to solve for the hypotenuse (r) Step 5: Use trig identities for sine, cosine, and tangent. Ex. Cosine is adj/hyp.

21. anonymous

the hypotenuse would be |dw:1438127320268:dw|

22. Zale101

|dw:1438127050766:dw|

23. Zale101

I'm sure you have completed all the four steps i gave above. Now, you are in the fifth step .