Question

find the exact values of sin apha, cos alpha, tan alpha, csc alpha, sec alpha, and cot alpha where is an angle in standard position whose terminal side contains the point 1,1.

Answer 1

To find the exact values of trigonometric functions for an angle in standard position whose terminal side contains the point (1,1), we use Pythagorean theorem to find the length of the hypotenuse and then apply the definitions of the functions.

Step-by-step explanation:

To find the exact values of trigonometric functions for an angle in standard position whose terminal side contains the point (1,1), we need to use the Pythagorean theorem to find the length of the hypotenuse. The length of the hypotenuse is given by the square root of the sum of the squares of the two sides, which in this case is sqrt(1^2 + 1^2) = sqrt(2).

Now, we can use the definitions of the trigonometric functions to find their exact values for this angle. We have sin(alpha) = Ay/A = 1/sqrt(2), cos(alpha) = Ax/A = 1/sqrt(2), tan(alpha) = Ay/Ax = 1, csc(alpha) = 1/sin(alpha), sec(alpha) = 1/cos(alpha), and cot(alpha) = 1/tan(alpha).