Trigonometric Values for Specific Angles

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Questions and Answers

What is the value of cos 30?

$\frac{\sqrt{3}}{2}$ (correct)

$\frac{\sqrt{2}}{2}$

$\frac{1}{2}$

What is the value of sin 30?

$\frac{1}{2}$

What is the value of cos 45?

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$ (correct)

What is the value of sin 45?

$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of cos 60?

$\frac{1}{2}$ Signup and view all the answers

What is the value of sin 60?

$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of cos 120?

-$\frac{1}{2}$ Signup and view all the answers

What is the value of sin 120?

$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of cos 135?

-$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of sin 135?

$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of cos 150?

-$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of sin 150?

$\frac{1}{2}$ Signup and view all the answers

What is the value of cos 210?

-$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of sin 210?

-$\frac{1}{2}$ Signup and view all the answers

What is the value of cos 225?

-$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of sin 225?

-$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of cos 240?

-$\frac{1}{2}$ Signup and view all the answers

What is the value of sin 240?

-$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of cos 300?

$\frac{1}{2}$ Signup and view all the answers

What is the value of sin 300?

-$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of cos 315?

$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of sin 315?

-$\frac{\sqrt{2}}{2}$ Signup and view all the answers

What is the value of cos 330?

$\frac{\sqrt{3}}{2}$ Signup and view all the answers

What is the value of sin 330?

-$\frac{1}{2}$ Signup and view all the answers

Study Notes

Trigonometric Values for Specific Angles

cos 30° equals √3/2, a vital cosine value for 30 degrees.
sin 30° equals 1/2, fundamental for understanding sine at this angle.
cos 45° equals √2/2, common for angles in the first quadrant.
sin 45° equals √2/2, indicating symmetry in sine and cosine at 45 degrees.
cos 60° equals 1/2, significant in determining cosine values of standard angles.
sin 60° equals √3/2, important for sine evaluations in the first quadrant.

Cosine and Sine in the Second Quadrant

cos 120° equals -1/2, demonstrates that cosine values in the second quadrant are negative.
sin 120° equals √3/2, consistent with sine being positive in the second quadrant.
cos 135° equals -√2/2, showing cosine remains negative in this quadrant.
sin 135° equals √2/2, following the positive sine rule in the second quadrant.
cos 150° equals -√3/2, reinforcing the trend of negative cosine values.
sin 150° equals 1/2, marking it as a positive sine value in the second quadrant.

Trigonometric Values for Angles in the Third Quadrant

cos 210° equals -√3/2, exemplifying negative cosine values in the third quadrant.
sin 210° equals -1/2, both sine and cosine are negative here.
cos 225° equals -√2/2, showing continued negativity for cosine.
sin 225° equals -√2/2, vital for calculations involving both sine and cosine.
cos 240° equals -1/2, consistent negative value for cosine in this quadrant.
sin 240° equals -√3/2, affirming the negative sine value.

Trigonometric Values in the Fourth Quadrant

cos 300° equals 1/2, highlighting that cosine values turn positive in the fourth quadrant.
sin 300° equals -√3/2, indicating a negative sine value.
cos 315° equals √2/2, mirrors the values of 45 degrees but positioned in the fourth quadrant.
sin 315° equals -√2/2, demonstrating the continuation of negative sine here.
cos 330° equals √3/2, again a positive cosine value characteristic of angles near the x-axis.
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.