Find the exact trigonometric function of cos(2a).
hyp: 17
opp: 15
adj: 8
assuming that your given triangle contains angle a
sina = 15/17, cosa = 8/17
cos(2a) = cos^2 a - sin^2 a
= ...
To find the exact trigonometric function of cos(2a), we need to use the given values of the hypotenuse (17), opposite side (15), and adjacent side (8) of a right triangle.
First, let's define the trigonometric function of cosine (cos). In a right triangle, cos(theta) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
cos(theta) = adjacent/hypotenuse
Let's use this definition to calculate the value of cos(a):
cos(a) = 8/17
Now, to find cos(2a), we need to use a double-angle identity for cosine, which states that:
cos(2a) = cos^2(a) - sin^2(a)
To find sin(a), we can use the given values of the opposite side and the hypotenuse:
sin(a) = opposite/hypotenuse = 15/17
Now, we have all the values needed to calculate cos(2a):
cos(2a) = cos^2(a) - sin^2(a)
Plugging in the values:
cos(2a) = (8/17)^2 - (15/17)^2
Let's simplify this equation:
cos(2a) = (64/289) - (225/289)
Now, subtract the fractions:
cos(2a) = -161/289
Therefore, the exact trigonometric function of cos(2a) is -161/289.