Table of contents

0. Review of College Algebra4h 45m

Rationalizing Denominators
17m

Pythagorean Theorem & Basics of Triangles
17m

Basics of Graphing
30m

Functions
41m

Transformations
45m

Asymptotes
4m

Solving Linear Equations
31m

Solving Quadratic Equations
55m

Complex Numbers
41m

1. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

2. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

3. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

4. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

6. Trigonometric Identities and More Equations2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

7. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

9. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

10. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

11. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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1:25 minutes

Problem 2.3.38

Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.
cos θ = 0.85536428

Verified step by step guidance

Identify the given equation: $\cos \theta = 0.85536428$ and the interval for $\theta$ is $[0^\circ, 90^\circ)$.

Recall that the cosine function is positive and decreasing in the first quadrant, so there will be one solution for $\theta$ in the given interval.

Use the inverse cosine function to find $\theta$: $\theta = \cos^{-1}(0.85536428)$.

Calculate the value of $\theta$ using a calculator set to degree mode to get the angle in degrees.

Round the result to six decimal places as required.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Cosine Function and Its Properties

The cosine function relates an angle in a right triangle to the ratio of the adjacent side over the hypotenuse. It is periodic and ranges between -1 and 1. Understanding its behavior on the interval [0°, 90°) is essential for finding the angle corresponding to a given cosine value.

Inverse Cosine (Arccos) Function

The inverse cosine function, denoted arccos or cos⁻¹, returns the angle whose cosine is a given number. It is used to find the angle θ when cos θ is known, typically producing results in the range [0°, 180°]. For this problem, restricting the solution to [0°, 90°) is important.

Decimal Degree Precision

Decimal degree precision refers to expressing angles in degrees with decimal points, allowing for more exact measurements. Here, answers must be given to six decimal places, which requires careful calculation and rounding to ensure accuracy.

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Master Example 1 with a bite sized video explanation from Patrick

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

tan θ = 6.4358841

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sin θ = 0.84802194

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sec θ = 1.1606249

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. cot θ = 0.21563481

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Textbook Question

Solve each problem. See Example 6. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec.

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Textbook Question

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"

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Multiple Choice

What is the angular position in radians of the minute hand of a clock at 3:30, measured from the 12 o'clock position in standard position (counterclockwise from the positive $x$ -axis)?

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