Ch. 5 - Trigonometric Identities

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 5 - Trigonometric Identities

Problem 5.RE.18

Chapter 6, Problem 5.RE.18

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 35°

Verified step by step guidance

Recall the co-function identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\).

Apply this identity to \(\sin 35^\circ\): rewrite it as \(\cos(90^\circ - 35^\circ)\).

Calculate the angle inside the cosine: \(90^\circ - 35^\circ = 55^\circ\).

Therefore, \(\sin 35^\circ\) is equivalent to \(\cos 55^\circ\).

Look for \(\cos 55^\circ\) in Column II to find the matching expression.

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Key Concepts

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

Basic Trigonometric Functions

Understanding sine, cosine, and tangent functions is fundamental. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse. Recognizing these functions helps in identifying equivalent expressions.

Trigonometric Identities

Trigonometric identities like the Pythagorean, co-function, and angle sum/difference identities allow rewriting expressions in different but equivalent forms. For example, sin(35°) can be related to cos(55°) using the co-function identity.

Co-function Identity

The co-function identity states that sin(θ) = cos(90° - θ). This is useful for converting sine expressions into cosine expressions and vice versa, enabling matching expressions from different columns that represent the same value.

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Pythagorean Identities

Related Practice

Textbook Question

Use the given information to find each of the following.

sin y, given cos 2y = -1/3 , π/2 < y < π

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Textbook Question

Use the given information to find the quadrant of x + y.

cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III

Textbook Question

Use the given information to find cos(x - y).

sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III

Textbook Question

For each expression in Column I, choose the expression from Column II that completes an identity.

6. sec² x = ____

A. sin ^2 x/cos ^2 x

B.1/(sec ^2 x)

C. sin (-x)

D. csc ^2 x-cot ^2 x + sin ^2 x

E. tan x

Textbook Question

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos(-55°)

Textbook Question

Use the given information to find sin(x + y).

sin y = - 2/3 , cos x = - 1/5, x in quadrant II, y in quadrant III

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.sin 35°

Verified video answer for a similar problem:

Key Concepts

Basic Trigonometric Functions

Trigonometric Identities

Co-function Identity

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 35°