Final answer:
To find the value of cos y° when sin y° = 9/c and tan y° = 9/d, we can use the trigonometric identity cos^2y + sin^2y = 1 and substitute the given values. Simplifying the equation, we can solve for cos y°.
Step-by-step explanation:
To find the value of cos y°, we can use the trigonometric identity:
cos^2y + sin^2y = 1
Given that sin y° = 9/c and tan y° = 9/d, we can substitute these values into the identity:
(9/c)^2 + (9/d)^2 = 1
Simplifying the equation, we have:
81/c^2 + 81/d^2 = 1
Multiplying both sides by c^2d^2, we get:
81d^2 + 81c^2 = c^2d^2
Dividing by 81, we obtain:
d^2 + c^2 = c^2d^2/81
Substituting cos^2y = c^2 and sin^2y = d^2, we have:
cos^2y + sin^2y = cos^2y + d^2 = c^2d^2/81
Now we can solve for cos y°:
cos y° = sqrt(c^2d^2/81 - d^2)