Answer:
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°
