Question

Suppose that a is an angle with sin A = 3/7 and a is not in the second quadrant. Compute the exact value of 10 a. You do not have to rationalize the denominator. Please answer it

Answer 1

The interpretation of '10a' is unclear in the context of the question. If referring to 10 times the angle A, no trigonometry is involved. If intending 10 times the sine value or the sine of 10 times angle A, the question needs clarification.

Step-by-step explanation:

The question involves determining the exact value of sin A given sin A = 3/7 and A is not in the second quadrant. To find 10a, we might assume the student is asking for sin(10 × A), but that interpretation seems unclear from the context provided. Instead, it seems there may be confusion in the question.

If considering simple multiplication by 10 (10 × A), the value would be 10 times the angle A, which doesn't involve any trigonometry or require the sine value. However, if the question intended to find 10 times the sine value, it would simply be the sine value multiplied by 10, giving 30/7, which is not a valid sine value as it's greater than 1.

If the question intended to ask for the sine of 10 times angle A, it would involve more complex trigonometry, such as using multiple angle identities from trigonometry, but such calculation isn't typically expressed in the form of '10a.'

Answer 2

The exact value of
`10\cdot a` is
`253.77^(\circ)`.

Step-by-step explanation:

Sine function is a bounded function between -1 and 1 and positive in the first and second quadrants. From statement we deduct that
`a` is in the first quadrant, that is,
`0^(\circ)< A < 90^(\circ)`. Then, we determine the angle by inverse trigonometric function:

`A = \sin^(-1) (3)/(7)`

`A \approx 25.377^(\circ)`

Then, the exact value of
`10\cdot a` is
`253.77^(\circ)`.