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kvasek [131]
2 years ago
5

Please help me do this question​

Mathematics
2 answers:
Gnom [1K]2 years ago
6 0

x = 90°, 16.3°

Step-by-step explanation:

We are going to use the identity

\cos x =\sqrt{1-\sin^2x}

and substitute this into our expression so we can write

4\sin x + 3\sqrt{1-\sin^2x} = 4

\Rightarrow 3\sqrt{1-\sin^2x} = 4(1 - \sin x)

Take the square of the equation above to get

9(1 - \sin^2x) = 16(1 - \sin x)^2

\:\:\:\:\:= 16(1 - 2\sin x +  \sin^2x)

Rearranging the terms, we then get

25\sin^2x - 32\sin x + 7 = 0

If we let u = \sin x, the above equation becomes

25u^2 - 32u + 7= 0

This looks like a quadratic equation whose roots are

u = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\;\;\;\;= \dfrac{32 \pm \sqrt{32^2 - 4(25)(7)}}{50}

\;\;\;\;=\dfrac{32 \pm 18}{50} = 1, 0.28

We can then write

\sin x = 1 \:\text{and}\;0.28

Solving for x, we finally get

x = 90°\:\text{and}\:16.3°

Minchanka [31]2 years ago
3 0

Answer:

Step-by-step explanation:

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