The point given below is on the terminal side of an angle θ in standard position. Find the exact value of each of the six trigonometric functions of θ. (-4,5)

Question

The point given below is on the terminal side of an angle θ in standard position. Find the exact value of each of the six trigonometric functions of θ. (-4,5)

Answer 1

Hello Judith,

The point given is in the form (x,y) where x = -4 and y = 5. You want to use the definition for each trig function, which you should have covered in class.

1. sin θ = y/r where r = √(x²+y²) = √(16+25) = √41 --> r = √41. Therefore: sin θ = 5/√41. If your class expects you to get rid of the square root in the denominator, you can turn the previous answer into sin θ = (5√41)/41
2. cos θ=x/r = -4/√41. Again, if you're expected to get rid of square root in the denominator, the answer would be cos θ = (-4√41)/41
3. tan θ = y/x = 5/-4 = -5/4 ---> tan θ = -5/4
4. cot θ = x/y = -4/5 ---> cot θ = -4/5
5. sec θ = r/x = √41/-4 = (- √41)/4 ---> sec θ = (- √41)/4
6. csc θ = r/y = √41/5 ---> csc θ = √41/5

Cheers!