Ok so I have a right triangle with the hypothenuse = to 5, one side =3 and the other =4 and X is the angle between the hypothenuse and the side that =3. I'm supposed to find the sin, cos, tan, cot, sec, csc of X. I can't seem to get the answer for the sec and csc. If sin(x)=4/5, csc then is 5/4 which shows error on the calculator. I'm getting the wrong answer.
To find the values of sec and csc, we first need to find the value of cos(x) and sin(x). From what you have provided, we already know that sin(x) = 4/5.
To find cos(x), we can use the Pythagorean identity, which states that sin^2(x) + cos^2(x) = 1. Since sin(x) = 4/5, we can solve for cos(x):
sin^2(x) + cos^2(x) = 1
(4/5)^2 + cos^2(x) = 1
16/25 + cos^2(x) = 1
cos^2(x) = 1 - 16/25
cos^2(x) = 9/25
Taking the square root of both sides, we find:
cos(x) = ±√(9/25) = ±(3/5)
Now, let's determine the correct sign of cos(x). Since the given triangle is a right triangle, cos(x) represents the adjacent side divided by the hypotenuse. In this case, the adjacent side is 3 and the hypotenuse is 5, so cos(x) = 3/5.
Now that we have the values of sin(x) = 4/5 and cos(x) = 3/5, we can calculate the remaining trigonometric ratios:
- tan(x) = sin(x)/cos(x) = (4/5)/(3/5) = 4/3
- cot(x) = 1/tan(x) = 1/(4/3) = 3/4
- sec(x) = 1/cos(x) = 1/(3/5) = 5/3
- csc(x) = 1/sin(x) = 1/(4/5) = 5/4
So, the correct values for sec(x) and csc(x) are 5/3 and 5/4, respectively.