Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the values of [tex]\(\cos 105^\circ\)[/tex] and [tex]\(\csc 105^\circ\)[/tex] given the values of [tex]\(\cos -105^\circ = -0.26\)[/tex] and [tex]\(\csc -105^\circ = -1.03\)[/tex], we can use the properties of trigonometric functions for negative angles. These properties are:
1. [tex]\(\cos(-\theta) = \cos(\theta)\)[/tex]
2. [tex]\(\csc(-\theta) = -\csc(\theta)\)[/tex]
Given:
[tex]\[ \cos(-105^\circ) = -0.26 \][/tex]
Using the identity for cosine of a negative angle:
[tex]\[ \cos 105^\circ = \cos(-105^\circ) \][/tex]
Therefore,
[tex]\[ \cos 105^\circ = -0.26 \][/tex]
Next, given:
[tex]\[ \csc(-105^\circ) = -1.03 \][/tex]
Using the identity for cosecant of a negative angle:
[tex]\[ \csc 105^\circ = -\csc(-105^\circ) \][/tex]
Therefore,
[tex]\[ \csc 105^\circ = 1.03 \][/tex]
So, we have:
[tex]\[ \cos 105^\circ = -0.26 \][/tex]
and
[tex]\[ \csc 105^\circ = 1.03 \][/tex]
1. [tex]\(\cos(-\theta) = \cos(\theta)\)[/tex]
2. [tex]\(\csc(-\theta) = -\csc(\theta)\)[/tex]
Given:
[tex]\[ \cos(-105^\circ) = -0.26 \][/tex]
Using the identity for cosine of a negative angle:
[tex]\[ \cos 105^\circ = \cos(-105^\circ) \][/tex]
Therefore,
[tex]\[ \cos 105^\circ = -0.26 \][/tex]
Next, given:
[tex]\[ \csc(-105^\circ) = -1.03 \][/tex]
Using the identity for cosecant of a negative angle:
[tex]\[ \csc 105^\circ = -\csc(-105^\circ) \][/tex]
Therefore,
[tex]\[ \csc 105^\circ = 1.03 \][/tex]
So, we have:
[tex]\[ \cos 105^\circ = -0.26 \][/tex]
and
[tex]\[ \csc 105^\circ = 1.03 \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.