sin x = -7 what is the value for x?

Question

Sorry This is really easy I'm just getting a big mind blank

Answer 1

you may be meaning sin x = - 1 ?
x = 3π / 2

Answer 2

Impossible. Absolute value of sin x never exceeds 1.

Answer 3

The maximum value of sin is + or - 1

Answer 4

punch in sin inverse (-7) into calculator. But yes, It never exceeds negative 1 or positive 1

Answer 5

Undefined as sin x cannot be above 1 and below -1.

Answer 6

The above answers are right. the sine of any number is always between -1 and 1.

This is because the sine of angle is the ratio of the length of the opposite side to the length of the hypotenuse. And the hypotenuse is always the longest side of a right triangle.

Answer 7

If you didn't know, the sin inverse is represented as sin^-1 on your calculator, and is on most calculators 2nd button, then sin.

Answer 8

hi

[e^(xi) - e^(-xi)] / 2i = 7
call u = e^(xi)

u - 1/u = 14 i
u^2 - 14 i u - 1 = 0
D^2 = (7i)^2 - (-1) = -49 + 1 = - 48

u = 7 i +/- √48 i
u = (+/- 4√3 + 7 ) i
u1 = ( 7 + 4√3 ) * e^ (π/2) i
u2 = ( 7 - 4√3 ) * e^ (π/2) i

then
x1 = 2 k π + π/2 - i ln ( 7 + 4√3 )
x2 = 2 k π + π/2 - i ln ( 7 - 4√3 )

Excel verified

greetings

Answer 9

--1

Answer 10

sin x = -7
2i sin x = -14i
2i sin x = exp(ix) - exp(-ix) = -14i
exp²(ix) - 1 = -14i exp(ix)
exp²(ix) + 14i exp(ix) - 1 = 0
(exp(ix) + 7i)² + 49 - 1 = 0
(exp(ix) + 7i)² = -48
exp(ix) + 7i = +/- 4√3 i
exp(ix) = -(7 +/- 4√3) i

ix = +/- ln(7 + √3) - π/2 i + 2πni

Answer:
x = (2πn - π/2) +/- i ln(7 + √3)