State the sine and cosine of two unique angles that do not fall on an axis where the values are the same positive value. Give the trig function and angle along with the values to so they are equivalent. Such as sin (___) = ___ and cos (___) = ___.

sin (30°) = 1/2 and cos (60°) = 1/2

Step-by-step explanation:

* Lets explain how to solve the problem

- In the first quadrant all the trigonometry functions are positive values

- We need two angles have same positive values of sine and cosine

- That means sin (x) = cos (y) = + ve value

∴ The two angles will lie on the first quadrant

- If sin (x) = cos (y), then angles x and y are complementary angles

- The sum of the measures of the complementary angles is 90°

∴ x + y = 90°

- In any right angle triangle

- Angle Ф is one of its acute angles, where Ф is opposite to the side

of length a, adjacent to the side of length b and c is the length of the

hypotenuse

- Angle β is the other acute angle, where β is opposite to the side

of length b, adjacent to the side of length a and c is the length of the

hypotenuse

- The sum of Ф and β is 90° ⇒ complementary angles

∵ sin Ф = opposite/hypotenuse

∵ cos Ф = adjacent/hypotenuse

∴ sin Ф = a/c and cos Ф = b/c ⇒ (1)

∵ sin β = opposite/hypotenuse

∵ cos β = adjacent/hypotenuse

∴ sin β = b/c and cos β = a/c ⇒ (2)

- From (1) and (2)

∴ sin Ф = cos β and cos Ф = sin β

* Now lets chose any two complementary angles

- If Ф = 30°, then β = 60°

∴ sin (30°) = 1/2

∴ cos (60°) = 1/2

* sin (30°) = 1/2 and cos (60°) = 1/2

# Remember you can chose any two angles their sum is 90°