How do i find cos[arctan(3/5)] ?
draw a triangle that matches those qualities
How do you set up the triangle? Once the triange is set up, then what do I do? How can I use the triangle to find the cos?
thanks
good lord, use google and be self reliant.......
To find cos[arctan(3/5)], you can use the concept of trigonometric identities. Here's how you can solve it step-by-step:
1. Start with the given expression: cos[arctan(3/5)].
2. Use the identity: tan(t) = opposite / adjacent. In this case, the opposite side is 3, and the adjacent side is 5. Therefore, tan(arctan(3/5)) = 3/5.
3. Since tan(arctan(x)) = x for any real number x, we can substitute tan(arctan(3/5)) with 3/5.
4. Now we have: cos[arctan(3/5)] = cos(arctan(3/5)).
5. Use another trigonometric identity: cos(arctan(x)) = 1 / sqrt(1 + x^2). Here, x represents 3/5.
6. Substitute x with 3/5: cos(arctan(3/5)) = 1 / sqrt(1 + (3/5)^2).
7. Simplify the expression: cos(arctan(3/5)) = 1 / sqrt(1 + 9/25) = 1 / sqrt(34/25).
8. Rationalize the denominator by multiplying the numerator and denominator by sqrt(25): cos(arctan(3/5)) = sqrt(25) / sqrt(34).
9. Simplify: cos(arctan(3/5)) = 5 / sqrt(34).
Thus, cos[arctan(3/5)] is equal to 5 / sqrt(34).