Question

Make this shorter and like a 9th grader wrote it In right triangle DOG, where angle O is 90 degrees, we have: sin ⁡ ( 7 0 ∘ ) = opposite hypotenuse = 𝑂 𝐺 𝐷 𝐺 sin(70 ∘ )= hypotenuse opposite​= DG OG​cos ⁡ ( 2 0 ∘ ) = adjacent hypotenuse = 𝑂 𝐺 𝐷 𝐺 cos(20 ∘ )= hypotenuse adjacent​= DG OG​Therefore, sin ⁡ ( 7 0 ∘ ) = cos ⁡ ( 2 0 ∘ ) sin(70 ∘ )=cos(20 ∘ ) because both are equal to the same ratio 𝑂 𝐺 𝐷 𝐺 DG OG​. This is because sine of an angle is equal to the cosine of its complement. The angles 70 degrees and 20 degrees are complementary, as they add up to 90 degrees. In general, sin ⁡ ( 𝑥 ) = cos ⁡ ( 9 0 ∘ − 𝑥 ) sin(x)=cos(90 ∘ −x) and cos ⁡ ( 𝑥 ) = sin ⁡ ( 9 0 ∘ − 𝑥 ) cos(x)=sin(90 ∘ −x).

Answer 1

In right triangle DOG with angle O = 90°, the other angles are 70° and 20° (they add to 90°).
For the 70° angle: sin(70°) = opposite/hypotenuse = OG/DG.
For the 20° angle: cos(20°) = adjacent/hypotenuse = OG/DG.

So sin(70°) = cos(20°) because both equal OG/DG.
In general, sin x = cos(90° − x).