there are certain special triangles that you can recognize by there angles. if the sin of the angle of a triangle is 1/2, basically you know that the opposite side of the triangle from the angle is 1 and the hypotenuse is 2. this means that the other side of the triangle has to be the square root of 3 (a^2 + b^2 = c^2). So therefore, the cosine of the angle, which is the adjacent side divided by the hypotenuse, must be (square root of 3)/2.
so since sin is opposite over hypotenuse, than the triangle made by your angle has one side of length 1 and the hypotenuse is length 2. therefore u can use pythagorean theoeom to find the length of the third side, or the adjacent side to theta, which ends up being 2^2-1= square root of 3. therefore since cos is adjacent over hypotenuse cos theta would be (root 3)/2
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cos θ = sqrt(1-sin^2 θ) = sqrt(1 - 1/4) = sqrt(3) / 2
there are certain special triangles that you can recognize by there angles. if the sin of the angle of a triangle is 1/2, basically you know that the opposite side of the triangle from the angle is 1 and the hypotenuse is 2. this means that the other side of the triangle has to be the square root of 3 (a^2 + b^2 = c^2). So therefore, the cosine of the angle, which is the adjacent side divided by the hypotenuse, must be (square root of 3)/2.
so since sin is opposite over hypotenuse, than the triangle made by your angle has one side of length 1 and the hypotenuse is length 2. therefore u can use pythagorean theoeom to find the length of the third side, or the adjacent side to theta, which ends up being 2^2-1= square root of 3. therefore since cos is adjacent over hypotenuse cos theta would be (root 3)/2
Knowing that the sin of the angle is 0.5, you can use the negative sin function on your calculator to determine the value of the angle.
sin-1 of 0.5 = 30
So the given angle is 30 degrees. Using your calculator, you can then determine that cos 30 = 0.866