Select all the correct answers.If the measure of angle is 𝜃 is 7𝜋4 , which statements are true? The measure of the reference angle is 60∘ . The measure of the reference angle is 30∘ . sin(𝜃)=-22 The measure of the reference angle is 45∘ . cos(𝜃)=-22 tan(𝜃)=-1
Question
Select all the correct answers.If the measure of angle is 𝜃 is 7𝜋4 , which statements are true? The measure of the reference angle is 60∘ . The measure of the reference angle is 30∘ . sin(𝜃)=-22 The measure of the reference angle is 45∘ . cos(𝜃)=-22 tan(𝜃)=-1
Solution
The measure of the angle 𝜃 is given as 7𝜋/4. This is equivalent to 315 degrees in the unit circle.
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The measure of the reference angle is 60∘: This statement is false. The reference angle for 315 degrees is 45 degrees.
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The measure of the reference angle is 30∘: This statement is false. The reference angle for 315 degrees is 45 degrees.
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sin(𝜃)=-22: This statement is false. The sine of any angle will always be between -1 and 1. Therefore, sin(𝜃) cannot be -22.
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The measure of the reference angle is 45∘: This statement is true. The reference angle for 315 degrees is 45 degrees.
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cos(𝜃)=-22: This statement is false. The cosine of any angle will always be between -1 and 1. Therefore, cos(𝜃) cannot be -22.
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tan(𝜃)=-1: This statement is true. The tangent of 315 degrees is -1.
So, the correct statements are "The measure of the reference angle is 45∘" and "tan(𝜃)=-1".
Similar Questions
(b)If ∠1 and ∠2 are complementary angles, then one of them must have a measure greater than 45°.=Counterexample:m∠1=, °m∠2°
The measure of angle θ is 7𝜋4. The measure of its reference angle is °, and tan θ is .
If ∠1 and ∠2 are complementary angles, then one of them must have a measure greater than 45°.
In △𝐴𝐵𝐶, 𝐴𝐵=6𝑐𝑚, 𝐴𝐶=12𝑐𝑚, 𝑚∠𝐴=60∘ and 𝐴𝐶― is the longest side. Which of the following statements about the measures of the angles in △𝐴𝐵𝐶 must be true? (Note: 𝑚∠𝑋 denotes the measure of angle X.)
Determine the reference angle for
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