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Inverse Trigonometric Functions

Short Answer Type

21. Find the principal values of the following

tan^-1(- 1)

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22. Find the principal values of the following

sec to the power of negative 1 end exponent open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses

133 Views

23. Find the principal values of the following

cot to the power of negative 1 end exponent open parentheses square root of 3 close parentheses

121 Views

24. Find the principal values of the following

cos to the power of negative 1 end exponent open parentheses negative fraction numerator 1 over denominator square root of 2 end fraction close parentheses

118 Views

25. Find the principal values of the following

cos e c to the power of negative 1 end exponent left parenthesis negative square root of 2 right parenthesis

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26. Evaluate

sin open square brackets 2 space cos to the power of negative 1 end exponent open parentheses negative 3 over 5 close parentheses close square brackets

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27. Evaluate sin[ tan^-1 (- 1) ]

sin[ tan^-1 (- 1) ] is a number lying between $straight pi over 2 space and space straight pi over 2$ [ by definition ]
and tan x = -1 when x = $negative straight pi over 4$
$therefore space space space space tan to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis space equals space minus straight pi over 4$
Now sin [ tan^-1 (- 1) = sin $open parentheses negative straight pi over 4 close parentheses equals negative fraction numerator 1 over denominator square root of 2 end fraction$