If cos 20=m determine the values of the following in terms of m. (a) cos(-200) (b)sin 250 (c)sin 20 thanks
can you not use the same name for all your posts?
cos(-200) = cos(200) = -cos(20) = -m
work with the other angles in a similar way. Draw triangles on the axes to help see the transformation formulas.
To determine the values of (a) cos(-200), (b) sin 250, and (c) sin 20 in terms of m, we will use the trigonometric identities and properties. Let's tackle each one separately:
(a) cos(-200):
To find cos(-200), we can use the fact that the cosine function is an even function, meaning that cos(-x) = cos(x) for any angle x. Therefore, cos(-200) is equal to cos(200). In terms of m, we substitute the given value: cos(200) = m.
(b) sin 250:
To determine sin 250, we can use the periodicity property of the sine function. This property states that sin(x) = sin(x + 360n) for any angle x and any integer n. In this case, we can rewrite sin 250 as sin(250 - 360) since subtracting 360 results in an angle in the same sine function period. In terms of m, we can substitute the given value: sin(250 - 360) = sin(-110) = -sin(110) = -√(1 - cos²(110)) = -√(1 - (m)²).
(c) sin 20:
To find sin 20, we can use the basic definition of the sine function. In terms of m: sin 20 = √(1 - cos²(20)) = √(1 - (m)²).
So, in summary:
(a) cos(-200) = m
(b) sin 250 = -√(1 - (m)²)
(c) sin 20 = √(1 - (m)²)