Find the remaining five trigonometric functions of θ. See Example 1. cosθ=-(1)/(4), sinθ>0

Name: Problem 38, Chapter 5: Trigonometry
Uploaded: 2022-10-18T23:43:51-08:00
Channel: Leslie Deeb
Description: Find the remaining five trigonometric functions of θ. See Example 1. cosθ=-(1)/(4), sinθ>0

step 1 Okay, let's figure out these first, these six trig functions. But before we do, we need to figur

Find the remaining five trigonometric functions of θ. See...

Key Concepts

Unit Circle

The unit circle is a fundamental tool in trigonometry that relates angles to points on a circle with a radius of one. It defines the sine and cosine of an angle as the y and x coordinates respectively, and helps in determining the values and signs of the trigonometric functions based on the quadrant in which the terminal side of the angle lies.

Quadrant Sign Determination

Determining the sign of a trigonometric function depends on which quadrant the angle is located in. For instance, if sin ? is positive while cos ? is negative, the angle lies in the second quadrant. This concept is crucial because the values of sine, cosine, and tangent (and their reciprocals) can be positive or negative depending on the quadrant.

Pythagorean Identity

The Pythagorean Identity, sin²? + cos²? = 1, is a key relationship in trigonometry that allows one to compute an unknown trigonometric function given another. In problems where one trigonometric function is known, this identity helps in finding the corresponding sine or cosine value, taking into account the correct sign based on the quadrant.

Trigonometric Reciprocals

Every primary trigonometric function has a reciprocal function: sine and cosecant, cosine and secant, tangent and cotangent. Understanding these relationships is essential for finding all six trigonometric functions when only one or two are initially provided.

Definition of Tangent and Cotangent

Tangent is defined as the ratio of sine to cosine, while cotangent is its reciprocal, the ratio of cosine to sine. This basic definition allows for the computation of these functions once sine and cosine are known, and it is particularly useful when their values are derived from the unit circle and Pythagorean identity.

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