Answer:
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Step-by-step explanation:
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Answer:
B) Sin^-1(-1) = 3pi/2 or 270°
D) Sin^-1(-1) = -pi/2 or -90°
Step-by-step explanation:
Sine function:
The sine function is -1 at 270º(-90º), which is 3pi/2 = -pi/2.
Inverse sine:
The input of the inverse sine function is a value, and the output are the angles which have the sine equal to the input.
Sin^-1(-1)
Angles for which the sine are -1, that is 3pi/2 or 270° and -pi/2 or -90°. Thus, options B and D are correct.
Cos x = -12/13
sin x = -sqrt(13^2 - 12^2) / 13 = -5/13
tan x = 5/12
tan x/2 = (1 - cos x) / sin x = 1 - (-12/13) / -5/13 = 25/13 * -13/5 = -5
2sin^2 x/2 = 1 - cos x = 1 - (-12/13) = 25/13
sin^2 x/2 = 25/13 / 2 = 25/26
sin x/2 = 5/√26
sin x/2 / cos x/2 = tan x/2
cos x/2 = sin x/2 / tan x/2 = 5/√26 / -5 = -1/√26
sin x/2 = 5/√26
cos x/2 = -1/√26
tan x/2 = -5