What is the value of cosθ, given that tanθ=8/3 and cosθ< 0? simplify radicals and rationalize the denominator, if necessary.

1. Check the picture below.

2. Tan∅=8/3 so let's construct the right triangle ABC with BC=8, BA=3, m(B)=90° and m(A) =∅. 

3. By Pythagorean theorem, AC=

4. cos∅=adjecent side/hypothenuse=

5. Cos∅ is negative so ∅ is in an angle in the second or third quadrant. The assumption that ∅ is and acute angle of a right triangle only makes the solution more practical. The only thing that changes, is sign, which depends on the quadrant.

6. As cos ∅ is negative, cos∅=- .

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!