Find the exact value of each of the remaining trigonometric functions of 0. 3 csc 0>0 tan 0 = sin 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cos 8 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) csc 8 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) sec 0 = (Simplify vour answer, including any radicals, Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise: Determining Exact Values of Trigonometric Functions**

Find the exact value of each of the remaining trigonometric functions of \( \theta \).

Given:
\[ 
\tan \theta = -\frac{3}{5}, \quad \csc \theta > 0 
\]

Calculate:

- \(\sin \theta =\) [Blank]
  
  *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*

- \(\cos \theta =\) [Blank]

  *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*

- \(\csc \theta =\) [Blank]

  *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*

- \(\sec \theta =\) [Blank]

  *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*

- \(\cot \theta =\) [Blank]

  *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*
Transcribed Image Text:**Exercise: Determining Exact Values of Trigonometric Functions** Find the exact value of each of the remaining trigonometric functions of \( \theta \). Given: \[ \tan \theta = -\frac{3}{5}, \quad \csc \theta > 0 \] Calculate: - \(\sin \theta =\) [Blank] *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)* - \(\cos \theta =\) [Blank] *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)* - \(\csc \theta =\) [Blank] *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)* - \(\sec \theta =\) [Blank] *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)* - \(\cot \theta =\) [Blank] *(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)*
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