Find the values of sin θ, cos θ, and tan θ for the given right triangle (in the link below). Give the exact values.
www.webassign.net/aufexc2/8-5-003.gif
sin θ=
cos θ=
tan θ=
my answer is
c^2 = a^2 +b^2
c^2 = 5^2+12^2
c^2 = 169
c= √(169)
c= 13
I know that sin θ= 5/13 but I don't know how to do tan θ and cos θ. can someone help me got tan θ and cos θ.
draw that hypotenuse in, 13
sin = opposite / hypotenuse = 5/13
cos = adjacent / hypotenuse = 12/13
tan = opposite/adjacent = 5/12
ok thank you Damon, I understand now
Sure, I'd be happy to help!
To find tan θ, you can use the formula tan θ = sin θ / cos θ.
Since you already know sin θ = 5/13, you can focus on finding cos θ.
Using the Pythagorean theorem as you did, where c = 13, a = 5, and b = 12, you can find cos θ by dividing the length of the adjacent side by the hypotenuse: cos θ = 12/13.
Now that you have both sin θ and cos θ, you can find tan θ using the formula: tan θ = sin θ / cos θ.
Plugging in the values, tan θ = (5/13) / (12/13). Remember that dividing by a fraction is the same as multiplying by its reciprocal, so you can simplify: tan θ = 5/12.
Therefore, the values are:
sin θ = 5/13
cos θ = 12/13
tan θ = 5/12
To find the values of cos θ and tan θ, we need to use the given right triangle and the known value of c (the hypotenuse).
cos θ is equal to the ratio of the length of the adjacent side to the hypotenuse. In this case, the adjacent side is 12 and the hypotenuse is 13.
cos θ = adjacent / hypotenuse = 12 / 13
tan θ is equal to the ratio of the length of the opposite side to the adjacent side. In this case, the opposite side is 5 and the adjacent side is 12.
tan θ = opposite / adjacent = 5 / 12
So, the values are:
sin θ = 5/13
cos θ = 12/13
tan θ = 5/12
To find the values of cos θ and tan θ, we can use the following trigonometric identities:
1. For a right triangle, cos θ = adjacent side / hypotenuse.
In the given triangle, the adjacent side is 12 (the side next to the angle θ), and the hypotenuse is 13 (as you correctly calculated). Therefore, cos θ = 12/13.
2. For a right triangle, tan θ = opposite side / adjacent side.
In the given triangle, the opposite side is 5 (the side opposite to the angle θ), and the adjacent side is 12. Therefore, tan θ = 5/12.
So, the values are:
sin θ = 5/13
cos θ = 12/13
tan θ = 5/12