Skip to main content
Ch. 3 - Trigonometric Identities and Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 3rd EditionCh. 3 - Trigonometric Identities and Equations문제 4
3장, 문제 4

In Exercises 1–6, use the figures to find the exact value of each trigonometric function. A right triangle labeled with sides 11, 60, and 61, and angle Δ, for trigonometric function exercises.
sin 2α

검증된 단계별 안내
1
Identify the given right triangle with sides 60, 11, and hypotenuse 61.
Recognize that the angle \( \alpha \) is opposite the side of length 11.
Use the double angle identity for sine: \( \sin 2\alpha = 2 \sin \alpha \cos \alpha \).
Calculate \( \sin \alpha = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{11}{61} \).
Calculate \( \cos \alpha = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{60}{61} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides. The primary functions include sine, cosine, and tangent, which are defined as ratios of the sides of a right triangle. For example, in a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse. Understanding these functions is essential for solving problems involving angles and side lengths.
추천 영상:
6:04
Introduction to Trigonometric Functions

Double Angle Formulas

Double angle formulas are trigonometric identities that express trigonometric functions of double angles in terms of single angles. For instance, the sine double angle formula states that sin(2α) = 2sin(α)cos(α). These formulas are useful for simplifying expressions and solving equations involving trigonometric functions, particularly when calculating values for angles that are multiples of a given angle.
추천 영상:
05:06
Double Angle Identities

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is crucial for finding missing side lengths in trigonometric problems and for verifying the relationships between the sides of a triangle.
추천 영상:
가이드 코스
5:19
Solving Right Triangles with the Pythagorean Theorem
관련 실천
교과서 질문

In Exercises 57–64, find the exact value of the following under the given conditions:

c. tan (α + β)

sin α = 3/5, α lies in quadrant I, and sin β = 5/13, β lies in quadrant II.

861
views
교과서 질문
Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. sin x cos 2x
824
views
교과서 질문
In Exercises 1–60, verify each identity. tan x csc x cos x = 1
936
views
교과서 질문

In Exercises 55–58, use the given information to find the exact value of each of the following:

c. tan(α/2)

tan α = 4/3, 180° < α < 270°

650
views
교과서 질문

In Exercises 55–58, use the given information to find the exact value of each of the following:

c. tan(α/2)

sec α = ﹣3, 𝝅/2 < α < 𝝅

632
views
교과서 질문
Use 105° = 135° - 30° to find the exact value of 105°.
829
views