Textbook Question
Determine whether each statement is true or false. See Example 4. cos 28° < sin 28° (Hint: sin 28° = cos 62°)
3. Unit Circle
Defining the Unit Circle
1:34 minutesProblem 51
Textbook Question
Give the exact value of each expression. See Example 5. sin 30°
Verified step by step guidance1
Recall the definition of the sine function in a right triangle: \(\sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}}\).
Recognize that 30° is a special angle in trigonometry, often associated with well-known exact values.
Use the known exact value for \(\sin 30^\circ\), which comes from the properties of a 30°-60°-90° triangle.
Recall that in a 30°-60°-90° triangle, the side opposite 30° is half the length of the hypotenuse.
Therefore, \(\sin 30^\circ = \frac{1}{2}\).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of the Sine Function
The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the hypotenuse. It is a fundamental trigonometric function used to relate angles to side lengths.
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Graph of Sine and Cosine Function
Special Angles and Their Exact Values
Certain angles like 30°, 45°, and 60° have well-known exact sine values derived from special triangles. For example, sin 30° equals 1/2, which is often memorized or derived from an equilateral triangle split in half.
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Using Reference Triangles to Find Exact Values
Reference triangles, such as the 30°-60°-90° triangle, help determine exact trigonometric values without a calculator. Understanding their side ratios allows for precise computation of sine, cosine, and tangent values.
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