If sinx= -4/5 and x terminates in quadrant 3 , find the exact value .

Question

Finding the value of -4/5 ... My mistake 

Answer 1

Problem: If sinx= -4/5 and x terminates in quadrant 3 , find the exact value of x.

Solution:

Since -π/2 ≤ sin^-1(z) ≤ π/2, -1 ≤ z ≤ 1, sin^-1(-4/5) is a negative angle in Quadrant IV.

 

The x we want is an angle in Quadrant 3, so x = π - sin^-1(-4/5) is the exact answer for one solution angle. If you use a calculator to evaluate x you get an approximate answer, x ≈ 4.06888787159141 radians. That's between 3.14 and 3(3.14)/2, so it's in quadrant 3.

 

Now, since the sine function is periodic with period 2π, the full answer to the problem is:

x = 2πn + π - sin^-1(-4/5) = π(2n+1) - sin^-1(-4/5), n integer. (Note that 2n+1 is an odd integer.)

Answer 2

Secant (Hypotenuse/Adjacent Side) is the reciprocal of the cosine (Adjacent Side/Hypotenuse).

Since Sine is Opposite Side/ Hypotenuse, use the Pythagorean Theorem to calculate the value of the opposite side of the right triangle:  5*5 = 4*4 + opposite side squared. 

25 = 16 + opposite side squared

Opposite side = 3

Since the problem is in the first quadrant, the sine is 3/5