Chapter 7: Q. 6 (page 500)

$°$ find the exact value of the expression
sin255 $°$ -sin15 $°$

Short Answer

Expert verified

sin255-sin15 $° = - 1.2247448714$

Step by step solution

Step 1. Rewriting the expression

$\sin (270 ° - x) = - \cos x \sin 255 ° = \sin (270 ° - 15 °) = - \cos 15 ° - \cos 15 ° = - \sin 75 ° o u r e x p r e s s i o n b e c o m e s \sin 255 ° - \sin 15 ° = - (\sin 75 ° + \sin 15 °)$

Step 2. calculations

Now our expression is $\sin 255 ° - \sin 15 ° = - (\sin 75 ° + \sin 15 °) \sin x + \sin y = 2 \sin (\frac{x + y}{2}) \cos (\frac{x - y}{2}) - (\sin 75 ° + \sin 15 °) = - 2 \sin 45 ° \cos 30 ° = - 2 \frac{1}{\sqrt{2}} \frac{\sqrt{3}}{2} = - 1.2247448714$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$°$ find the exact value of the expression
sin255 $°$ -sin15 $°$

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Decision Maths

Discrete Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

°find the exact value of the expression sin255°-sin15°

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Decision Maths

Discrete Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

$°$ find the exact value of the expression
sin255 $°$ -sin15 $°$