Questions and Answers
What is the value of cos 30?
What is the value of sin 30?
$\frac{1}{2}$
What is the value of cos 45?
What is the value of sin 45?
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What is the value of cos 60?
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What is the value of sin 60?
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What is the value of cos 120?
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What is the value of sin 120?
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What is the value of cos 135?
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What is the value of sin 135?
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What is the value of cos 150?
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What is the value of sin 150?
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What is the value of cos 210?
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What is the value of sin 210?
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What is the value of cos 225?
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What is the value of sin 225?
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What is the value of cos 240?
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What is the value of sin 240?
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What is the value of cos 300?
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What is the value of sin 300?
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What is the value of cos 315?
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What is the value of sin 315?
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What is the value of cos 330?
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What is the value of sin 330?
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Study Notes
Trigonometric Values for Specific Angles
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cos 30° equals √3/2, a vital cosine value for 30 degrees.
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sin 30° equals 1/2, fundamental for understanding sine at this angle.
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cos 45° equals √2/2, common for angles in the first quadrant.
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sin 45° equals √2/2, indicating symmetry in sine and cosine at 45 degrees.
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cos 60° equals 1/2, significant in determining cosine values of standard angles.
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sin 60° equals √3/2, important for sine evaluations in the first quadrant.
Cosine and Sine in the Second Quadrant
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cos 120° equals -1/2, demonstrates that cosine values in the second quadrant are negative.
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sin 120° equals √3/2, consistent with sine being positive in the second quadrant.
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cos 135° equals -√2/2, showing cosine remains negative in this quadrant.
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sin 135° equals √2/2, following the positive sine rule in the second quadrant.
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cos 150° equals -√3/2, reinforcing the trend of negative cosine values.
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sin 150° equals 1/2, marking it as a positive sine value in the second quadrant.
Trigonometric Values for Angles in the Third Quadrant
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cos 210° equals -√3/2, exemplifying negative cosine values in the third quadrant.
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sin 210° equals -1/2, both sine and cosine are negative here.
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cos 225° equals -√2/2, showing continued negativity for cosine.
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sin 225° equals -√2/2, vital for calculations involving both sine and cosine.
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cos 240° equals -1/2, consistent negative value for cosine in this quadrant.
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sin 240° equals -√3/2, affirming the negative sine value.
Trigonometric Values in the Fourth Quadrant
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cos 300° equals 1/2, highlighting that cosine values turn positive in the fourth quadrant.
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sin 300° equals -√3/2, indicating a negative sine value.
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cos 315° equals √2/2, mirrors the values of 45 degrees but positioned in the fourth quadrant.
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sin 315° equals -√2/2, demonstrating the continuation of negative sine here.
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cos 330° equals √3/2, again a positive cosine value characteristic of angles near the x-axis.
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sin 330° equals -1/2, signifying the return of negative sine values in the fourth quadrant.
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Description
This quiz covers the fundamental trigonometric values of sine and cosine for specific angles, including 30°, 45°, 60°, 120°, 135°, and 150°. Understanding these values is crucial for mastering the concepts of trigonometry, particularly in the context of the unit circle and angle quadrants.
