V3use the trigonometric identities to find the exact value of each of the following.Given cos 30°%3D(a) sin 60° (b) sin 230° (c) sec* (d) csc 3(a) sin 60°(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressic%3D

Name: V3use the trigonometric identities to find the exact value of each of
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: V3use the trigonometric identities to find the exact value of each of the following.Given cos 30°%3D(a) sin 60° (b) sin 230° (c) sec* (d) csc 3(a) sin 60°(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the

Answered: (a) sin 60° (b) sin 30° (c) sec 6

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 64RE

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

V3
use the trigonometric identities to find the exact value of each of the following.
Given cos 30°
%3D
(a) sin 60° (b) sin 230° (c) sec
* (d) csc 3
(a) sin 60°
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressic
%3D

Expert Solution

Step 1

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to be solved.”.

(a)

We have

$\begin{array}{rcl} \sin^{2} 30 + \cos^{2} 30 & = & 1 \\ \Rightarrow & \sin^{2} 30 = 1 - \cos^{2} 30 \\ = & 1 - {(\frac{\sqrt{3}}{2})}^{2} \\ = & 1 - \frac{3}{4} \end{array} = \frac{1}{4} . . . . . . (1) \Rightarrow \sin 30 = \frac{1}{2}$

Now

$\begin{array}{rcl} \sin 60 & = & \sin (2 \cdot 30) \\ = & 2 (\sin 30) (\cos 30) \\ = & 2 (\frac{1}{2}) (\frac{\sqrt{3}}{2}) \\ = & \frac{\sqrt{3}}{2} \end{array}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamentals of Trigonometric Identities$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions