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3 years ago

What is the value of the angle marked with x?

Mathematics

1 answer:

DaniilM [7]3 years ago

6 0

Answer:

132°

Step-by-step explanation:

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Solve the equation for principal values of x. Express solutions in degrees.

Hitman42 [59]

Option C:

x = 90°

Solution:

Given equation:

$\sin x=1+\cos ^{2} x$

<u>To find the degree:</u>

$\sin x=1+\cos ^{2} x$

Subtract 1 + cos²x from both sides.

$\sin x-1-\cos ^{2} x=0$

Using the trigonometric identity: $\cos ^{2}(x)=1-\sin ^{2}(x)$

$\sin x-1-\left(1-\sin ^{2}x\right)=0$

$\sin x-1-1+\sin ^{2}x=0$

$\sin x-2+\sin ^{2}x=0$

$\sin ^{2}x+\sin x-2=0$

Let sin x = u

$u^2+u-2=0$

Factor the quadratic equation.

$(u+2)(u-1)=0$

u + 2 = 0, u – 1 = 0

u = –2, u = 1

That is sin x = –2, sin x = 1

sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.

sin x = 1

The value of sin is 1 for 90°.

x = 90°.

Option C is the correct answer.

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Suppose we choose $x=1$ and $y=\dfrac12$ . Then

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Now suppose we choose $x,y$ such that

$\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}$

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I have attached a diagram of the triangle described.

We can use any of the trigonometric functions to find angle x. Remember, SOH CAH TOA. And since we're finding the angle, we'll need to use an inverse trigonometric function. For this problem, I'll be using the sine function.

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Hope this helps!! :)

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