What is the equivalent cosine of the acute angle in a right triangle if the sine of its adjacent angle is 0.759?
To find the equivalent cosine of the acute angle in a right triangle, we need to use the relationship between sine and cosine in trigonometry.
The sine of an acute angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the sine of the adjacent angle is given as 0.759.
Let's use the Pythagorean identity in a right triangle: sin^2(theta) + cos^2(theta) = 1, where theta is the angle in question.
Since we know the sine of the adjacent angle is 0.759, we can substitute it into the equation:
0.759^2 + cos^2(theta) = 1
Simplifying the equation:
0.576081 + cos^2(theta) = 1
Next, we can solve for cos^2(theta) by subtracting 0.576081 from both sides:
cos^2(theta) = 1 - 0.576081
cos^2(theta) = 0.423919
Now we can find the square root of both sides to get the cosine of the acute angle:
cos(theta) = √(0.423919)
Using a calculator, we find that cos(theta) is approximately 0.651.
Therefore, the equivalent cosine of the acute angle in the right triangle, given that the sine of its adjacent angle is 0.759, is approximately 0.651.
To find the equivalent cosine of the acute angle in a right triangle, we can use the relationship between sine and cosine in a right triangle.
Given that the sine of the adjacent angle is 0.759, we can use the reciprocal function to find the cosine:
cosine = 1 / (sine)
Hence, the equivalent cosine of the acute angle in the right triangle is:
cosine = 1 / 0.759
Evaluating it:
cosine ≈ 1.317