Question

If y = 4+9 sin 5x then which holds good?

a) -5 ≤ y ≤ 13

b) -4 sys8

c) -5<y<5

d) 0 <y <1
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Answer 1

Step-by-step explanation:

$\tt\red{QUESTION}$$\tt\blue{::}$

If y = 4+9 sin 5x then which holds good?

$\tt\red{ANSWER}$$\tt\blue{::}$

4 * 2^sin(x) = 3 * 3^cos(x)

2^(2+sin(x)) = 3^(1 + cos(x))

take the log:

(2+sin(x))*ln(2) = (1 + cos(x)) * ln(3)

(2+sin(x)) *ln(2)/ln(3) - 1 = cos(x) = sqrt(1-sin^2(x))

Let y = sin(x)

(2+y)*ln(2)/ln(3) -1 = sqrt(1-y^2)

Square both sides to give a quadratic equation in y.

I leave it to you to solve using the quadratic formula and remember that x = asin(y).

Answer 2

Answer:

a) -5 ≤ y ≤ 13

Step-by-step explanation:

y = 4+9 sin 5x

The range of sin A  is -1 ≤ sin A ≤  1.

So when  the sine is -1 we have

y = 4 + 9*-1

= -5

and when it is 1 we have:

y = 4 + 9 = 13

So the answer is a).