Find all angles θbetween 0^∘ and 180^∘ satisfying the given equation. cosθ=0.7

Name: Problem 25, Chapter 6: Algebra and Trigonometry
Uploaded: 2020-07-22T08:02:59-08:00
Duration: 1 min 22 s
Channel: Kevin Luu
Description: Find all angles θbetween 0^∘ and 180^∘ satisfying the given equation. cosθ=0.7

step 1 So here we have, we have the problem cosine theta equals equal, is equal to point seven. And we

Find all angles θbetween 0^∘ and 180^∘ satisfying the given...

Key Concepts

Cosine Function

The cosine function is a fundamental trigonometric function that relates an angle to the ratio of the adjacent side to the hypotenuse in a right triangle. It is defined for all real numbers and exhibits periodicity, meaning that its values repeat every full rotation (360° or 2? radians). The cosine function also shows symmetry, being an even function where cos(?) = cos(??). This property is essential in finding multiple angles that yield the same cosine value.

Inverse Cosine (Arccosine)

The inverse cosine function, commonly denoted as arccos, is used to determine the principal angle whose cosine equals a given value. It outputs angles in the range of 0° to 180° (or 0 to ? radians). This is particularly important when solving equations of the form cos(?) = a, as it provides the primary solution, from which additional solutions may be deduced based on the properties of the cosine function.

Unit Circle and Angle Quadrants

The unit circle is a key conceptual tool in trigonometry that helps visualize how angle measures correspond to coordinates on a circle with a radius of one. It clarifies the relationship between angles and their sine and cosine values, and highlights which quadrants yield positive or negative values for these functions. This quadrant analysis is crucial when determining all possible angles satisfying a trigonometric equation, especially within a specified interval.

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