Find the angle [OA] makes with the positive x-axis if the x-coordinate of the point A on the unit circle is 0.222
1 answer:
By using the concepts of <em>unit</em> circle and <em>trigonometric</em> functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
<h3>How to find an angle in an unit circle</h3>
<em>Unit</em> circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and <em>trigonometric</em> functions related to them. If we use <em>rectangular</em> coordinate system and the definition of the <em>tangent</em> function, we find that the angle OA is equal to:
tan θ ≈ 77.173°
By using the concepts of <em>unit</em> circle and <em>trigonometric</em> functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
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The true statements about the diagram given are:
3. m∠JKL = 45°
4. m∠MKQ + m∠PKQ = m∠PKM
5. PK is an angle bisector
<h3>What is an Angle Bisector?</h3>An angle bisector is a segment that divides a given angle into two parts that are congruent to each other.
The missing part of the question is in the image attached below.
In the image given, PK bisects the straight angle JKM since angles JKP and MKP both equal 90 degrees (right angle).
Therefore, m∠JKL = m∠PKL = 45°
m∠MKQ + m∠PKQ = m∠PKM based on the angle addition theorem.
Therefore, the true statements are:
3. m∠JKL = 45°
4. m∠MKQ + m∠PKQ = m∠PKM
5. PK is an angle bisector
(see image attached below)
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