Textbook Question
Give the exact value of each expression. See Example 5. tan 30°
Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 3, Problem 51
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, \(\sin 30^\circ = \frac{1}{2}\).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key 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.
Recommended video:
5:53
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.
Recommended video:
04:3945-45-90 Triangles
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.
Recommended video:
5:31Reference Angles on the Unit Circle
Related Practice
Textbook Question
Give the exact value of each expression. See Example 5. cos 30°
Textbook Question
Determine whether each statement is true or false. See Example 4. csc 20° < csc 30°
Textbook Question
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Height of a Tower The angle of depression from a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. Find the height of the tower.
2
views
Textbook Question
Solve each problem.See Examples 3 and 4. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?
1
views
Textbook Question
Solve each problem. See Examples 1–4. Altitude of a Triangle Find the altitude of an isosceles triangle having base 184.2 cm if the angle opposite the base is 68°44'.
5
views