Answer:
tan theta = 3/4
cot theta = 4/3
sin theta = 3/5
csc theta = 5/3
cos theta 4/5
sec theta = 5/4
Explanation:
Since this is a right triangle, we can use trig functions
We know the adjacent side and the opposite side so we will use the tangent function
tan theta = opposite/ adjacent
tan theta = 6/8
tan theta = 3/4
cot theta = adjacent / opposite = 8/6 = 4/3
Now we need to find the hypotenuse, using the pythagorean theorem
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36+64 = c^2
100 =c^2
Taking the square root
sqrt(100) = sqrt(c^2)
10 = c
The hypotenuse = 10
sin theta = opposite / hypotenuse
sin theta = 6/10 = 3/5
csc theta = hypotenuse / opposite = 10/6 = 5/3
cos theta = adjacent/ hypotenuse = 8/10 = 4/5
sec theta = hypotenuse/adjacent = 10/8 = 5/4