Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find the value of [tex]\( x \)[/tex] for which [tex]\(\cos(x) = \sin(14^\circ) \)[/tex] within the range [tex]\( 0^\circ < x < 90^\circ \)[/tex], we can use a fundamental trigonometric identity.
The identity states that:
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
for any angle [tex]\(\theta\)[/tex].
Given [tex]\(\sin(14^\circ)\)[/tex], we need [tex]\(\cos(x)\)[/tex] to be equal to [tex]\(\sin(14^\circ)\)[/tex]. Using the identity, we can write:
[tex]\[ \sin(14^\circ) = \cos(90^\circ - 14^\circ) \][/tex]
Thus, if [tex]\(\cos(x) = \sin(14^\circ)\)[/tex], we must have:
[tex]\[ x = 90^\circ - 14^\circ \][/tex]
So, calculating this gives:
[tex]\[ x = 90^\circ - 14^\circ = 76^\circ \][/tex]
Therefore, the value of [tex]\( x \)[/tex] for which [tex]\(\cos(x) = \sin(14^\circ) \)[/tex] is [tex]\( 76^\circ \)[/tex]. Hence, the correct answer is:
[tex]\[ \boxed{76^\circ} \][/tex]
The identity states that:
[tex]\[ \sin(\theta) = \cos(90^\circ - \theta) \][/tex]
for any angle [tex]\(\theta\)[/tex].
Given [tex]\(\sin(14^\circ)\)[/tex], we need [tex]\(\cos(x)\)[/tex] to be equal to [tex]\(\sin(14^\circ)\)[/tex]. Using the identity, we can write:
[tex]\[ \sin(14^\circ) = \cos(90^\circ - 14^\circ) \][/tex]
Thus, if [tex]\(\cos(x) = \sin(14^\circ)\)[/tex], we must have:
[tex]\[ x = 90^\circ - 14^\circ \][/tex]
So, calculating this gives:
[tex]\[ x = 90^\circ - 14^\circ = 76^\circ \][/tex]
Therefore, the value of [tex]\( x \)[/tex] for which [tex]\(\cos(x) = \sin(14^\circ) \)[/tex] is [tex]\( 76^\circ \)[/tex]. Hence, the correct answer is:
[tex]\[ \boxed{76^\circ} \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.