Find the exact value of tan(sin^ -1((-4/5))?

Question

Find the exact value of tan(sin^ -1((-4/5))

Answer 1

The best way to do these types of problems is to draw a right triangle then label one of the angles (not the right angle) theta.
arcsin(-4/5) gives you an angle theta such that sin(theta) = -4/5.
Label your triangle such that sin(theta) = -4/5.
The hypoteneuse will be 5 and the leg opposite theta will be -4. Use the pythagorean formula to find the length of the other side of the triangle (3).
Now you can use the triangle to find tan(theta).
tan(theta) = -4/3

This is your answer, -4/3

Answer 2

A) Pythagoras' theorem an exact triangle with hypotenuse 5 one area 4 ( considering the fact that cosine is 4/5) has the 0.33 area 3. The cosine makes use of the backside, so base area is 4. So tan is 3/4. B) This has V3 because of the fact the perpendicular and a million as base so tan is squarert. 3 or a million.732. by the way, the triangle is an equilateral triangle halved by ability of its perpendicular bisector, so perspective is 60 levels.

Answer 3

tan(sin^-1 (-4/5)) = sin(sin^-1 (-4/5))/cos(sin^-1 (-4/5)) =
= (-4/5)/ +- sqrt(1 - (4/5)^2) = (-4/5) / +- sqrt(1 - 16/25) =
= (-4/5) / +- sqrt(9/25) = (-4/5)/+-(3/5) = +- 4/3

Now, let's decide if we take the positive or negative value:
Because the range of sin^-1 is -pi/2 to pi/2
cos (x) for x in (-pi/2, pi/2) is greater than zero.
Thus, we take cos(sin^-1(-4/5) = 3/5

and tan(sin^ -1((-4/5)) = (-4/5)/(3/5) = -4/3 = -1 1/3

Answer 4

-1 1/3

Answer 5

-4/3
since
=tan(sin^ -1((-4/5))
=sin(sin^ -1((-4/5))/cos(sin^ -1((-4/5))
=-(4/5)/sqrt(1-sin(sin^ -1((-4/5)))^2)
=(4/5)/sqrt(1-(-4/5)^2)
=-(4/5)/((+/-).6)
=(+/-)(4/3)
and tan is negative in that quadrant

Answer 6

^ mean sin inverse to u is it? if that so the ans is1.33
if it just mean sin the ans is 0.87.

Answer 7

1.33

dont u have a calc...