Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Find the exact value of the expression. Write the answer as a single fraction. Do not use a calculator.
[tex]sin \frac{3 \pi }{2} tan (\frac{-23 \pi }{4}) - cos (\frac{-10 \pi }{3}) [/tex]
Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.

Sagot :

[tex]Use:\\sin(x+y)=sinxcosy+sinycosx\\\\tan(-x)=-tanx\\tan(k\pi+x)=tanx\\\\cos(-x)=cosx\\cos(2k\pi+x)=cosx\\cos(x+y)=cosxcosy-sinxsiny[/tex]


[tex]sin\frac{3\pi}{2}=sin(\pi+\frac{\pi}{2})=sin\pi cos\frac{\pi}{2}+sin\frac{\pi}{2} cos\pi=0\cdot0+1\cdot(-1)=-1\\\\tan\left(-\frac{23\pi}{4}\right)=-tan\frac{23\pi}{4}=-tan\left[6\pi+\left(-\frac{1}{4}\pi\right)\right]=-tan\left(-\frac{1}{4}\pi\right)=tan\frac{\pi}{4}=1[/tex]

[tex]cos\left(-\frac{10\pi}{3}\right)=cos\frac{10\pi}{3}=cos\left(2\pi+1\frac{1}{3}\pi\right)=cos\left(1\frac{1}{3}\pi\right)=cos\left(\pi+\frac{\pi}{3}\right)\\=cos\pi cos\frac{\pi}{3}-sin\pi sin\frac{\pi}{3}=-1\cdot\frac{1}{2}-0\cdot\frac{\sqrt3}{2}=-\frac{1}{2}\\\\sin\frac{3\pi}{2}tan\left(-\frac{23\pi}{4}\right)-cos\left(-\frac{10\pi}{3}\right)=-1\cdot1-\left(-\frac{1}{2}\right)=-1+\frac{1}{2}=-\frac{1}{2}[/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.