Question

Use the given information to find the exact function value. Simplify your answer as much as possible. Rationalize the denominator if necessary:

cos(a) = 12/13, 3π/2

Answer 1

To find the sine of angle a, with cos(a) = 12/13, use the Pythagorean identity to calculate sin(a) = √(1 - cos^2(a)) which gives us sin(a) = 5/13 after simplifying.

Step-by-step explanation:

The student provided information, "cos(a) = 12/13", points us to use trigonometric identities and properties to find the exact value of another function involving the angle a. Given the context, it seems the student might be seeking the sine of a or another related function. Since a cosine of 12/13 suggests a right-angled triangle where the adjacent side is 12, the hypotenuse is 13, and using the Pythagorean theorem, we can find the opposite side.

To find the sine, we use the formula sin(a) = √(1 - cos2(a)). Substituting the given cosine value:

sin(a) = √(1 - (12/13)2)
sin(a) = √(1 - 144/169)
sin(a) = √(25/169)
sin(a) = 5/13.

The student should ensure the angle a is in the correct quadrant to determine the sign of the sine value.