/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 In \(3-44,\) find the exact valu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 35

In \(3-44,\) find the exact value. $$ \sin 90^{\circ}+\cos 0^{\circ}+\tan 45^{\circ} $$

Short Answer

Expert verified
The exact value is 3.

Step by step solution

01

Understanding Trigonometric Functions

Firstly, recognize and recall the basic trigonometric values for the angles given. Specifically, we use the fact that \( \sin 90^\circ = 1 \), \( \cos 0^\circ = 1 \), and \( \tan 45^\circ = 1 \).
02

Evaluate Each Trigonometric Function

Calculate each of the given trigonometric expressions: \( \sin 90^\circ = 1 \), \( \cos 0^\circ = 1 \), and \( \tan 45^\circ = 1 \).
03

Sum the Values

Add the values from the previous step: \( 1 + 1 + 1 = 3 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Trigonometric Values
Understanding basic trigonometric values is crucial for solving many problems in trigonometry. There are certain standard angles which provide easy-to-remember trigonometric values:
  • The sine of 90掳 is 1. This means when a right angle is made, the sine function identifies the vertical or 'opposite' length as being equal to the hypotenuse.
  • The cosine of 0掳 is 1. At 0掳, the cosine measures how far along the horizontal axis you are, which is all the way to the beginning of the axis.
  • The tangent of 45掳 is 1. This indicates that both the vertical and horizontal lengths are equal, making the slope or tangent 1.
These basic values form the foundation for more complex calculations and are worth remembering.
Angle Measures
Angles help determine the values of trigonometric functions. Most trigonometric problems involve either degrees or radians.
  • Degrees are more intuitive and based on dividing a circle into 360 parts. An angle of 90掳 is a quarter of the circle, 45掳 is an eighth, and so on.
  • Radians provide a more mathematically natural measure, rooted in the properties of circles. For example, 90掳 is equivalent to \( \frac{\pi}{2} \) radians, and 45掳 is \( \frac{\pi}{4} \).
Understanding the unit of measurement for your angles ensures you interpret trigonometric functions correctly. Working with degrees is often simpler for basic problems, while radians are useful for calculus and advanced studies.
Trigonometric Identities
Trigonometric identities are equations that are true for all angles, forming the backbone of trigonometric proofs and simplifications.
  • Pythagorean Identity: This includes \( \sin^2 \theta + \cos^2 \theta = 1 \). This identity helps in connecting functions for any angle measure.
  • Angle Sum and Difference Identities: Functions like sine and cosine can be expressed as the sum or difference, for example, \( \sin(A \pm B) \).
  • Reciprocal and Ratio Identities: Involve \( \csc \theta, \sec \theta, \cot \theta \), which are inverses such as \( \csc \theta = \frac{1}{\sin \theta} \).
Mastering these identities acts like a toolbox, enabling you to simplify trigonometric expressions, solve equations, and prove other identities effortlessly.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\cos \theta=0.6283\)

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \sin \theta=0.9990 $$

Use an equilateral triangle with sides of length 4 to find the exact values of \(\sin 30^{\circ}, \cos 30^{\circ},\) and \(\tan 30^{\circ} .\)

Use a counterexample to show that \(A < B\) implies cos \(A < \cos B\) is false.

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=0.2126 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.