if sec a = -9/7 and tan a = - 4√2/7 , find csc a

Question

Use quotient and reciprocal identities to find the function value.

Answer 1

cos a = 1/sec a

if sec a = -9/7, then cos a = -7/9

tan a = sin a/cos a

-4sqrt(2)/7 = sin a / -7/9

sin a = -4sqrt(2) * -7 = 4sqrt(2)

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7 9 9

csc a = 1/sina = 9 = 9 sqrt(2)

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4sqrt(2) 8