Question

Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(4, 5) sin = (4√41)/41 (5√41)/41 4/5 5/4 what is the correct answer

Answer 1

Ok One side would have a length of 4, another side would have a length of 5, and then we can use the Pythagorean Theorem to find the length of the hypotenuse. a^2 + b^2 = c^2 

a=4; b=5; 

4^2 + 5^2 = c^2 
16 + 25 = c^2 
41 = c^2 
c = √41 

Therefore, the hypotenuse has a length of √41. 

To find the sinθ, you take the opposite over the hypotenuse. 

Remember when you drew out the triangle? θ is the angle connected to the origin. The opposite side is b, which is 5. 

Your answer is 5/√41. 

This answer must be simplified since there is a radical in the denominator. To simplify, you can just multiply the numerator and the denominator by √41/√41 (since this is equivalent to 1). 

This gives you the answer