Answered

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For what value of [tex]x[/tex] is [tex]\sin (x) = \cos \left(32^{\circ}\right)[/tex], where [tex]0^{\circ} \ \textless \ x \ \textless \ 90^{\circ}[/tex]?

A. [tex]64^{\circ}[/tex]
B. [tex]58^{\circ}[/tex]
C. [tex]32^{\circ}[/tex]
D. [tex]13^{\circ}[/tex]

Sagot :

GinnyAnswer
Sure! Let's dive into solving the problem step-by-step.

Given the equation:
[tex]\[ \sin(x) = \cos(32^\circ) \][/tex]
we want to find the value of \( x \) such that \( 0^\circ < x < 90^\circ \).

We can use the trigonometric identity:
[tex]\[ \sin(x) = \cos(90^\circ - x) \][/tex]
According to this identity, if \( \sin(x) = \cos(32^\circ) \), then it means:
[tex]\[ x = 90^\circ - 32^\circ \][/tex]

Now, let's perform the subtraction:
[tex]\[ x = 90^\circ - 32^\circ = 58^\circ \][/tex]

Therefore, the value of \( x \) is:
[tex]\[ \boxed{58^\circ} \][/tex]

So, the answer is B. [tex]\( 58^\circ \)[/tex].
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